swapnil7777/calc_9_12_2024 · Datasets at Hugging Face

question stringlengths 34 108	steps stringlengths 81 639	answer stringlengths 11 162
Integrate the equation cos(1*x + 4)	Let u = 1x + 4, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1x + 4 to get (1/1) * sin(1*x + 4). Finally, add the constant of integration C.	(1/1) * sin(1*x + 4) + C
Integrate the equation cos(7*x + 8)	Let u = 7x + 8, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7x + 8 to get (1/7) * sin(7*x + 8). Finally, add the constant of integration C.	(1/7) * sin(7*x + 8) + C
Integrate the equation cos(5*x + 3)	Let u = 5x + 3, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5x + 3 to get (1/5) * sin(5*x + 3). Finally, add the constant of integration C.	(1/5) * sin(5*x + 3) + C
Integrate the equation cos(9*x + 0)	Let u = 9x + 0, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9x + 0 to get (1/9) * sin(9*x + 0). Finally, add the constant of integration C.	(1/9) * sin(9*x + 0) + C
Integrate the equation cos(7*x + -2)	Let u = 7x + -2, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7x + -2 to get (1/7) * sin(7*x + -2). Finally, add the constant of integration C.	(1/7) * sin(7*x + -2) + C
Integrate the equation cos(2*x + -8)	Let u = 2x + -8, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2x + -8 to get (1/2) * sin(2*x + -8). Finally, add the constant of integration C.	(1/2) * sin(2*x + -8) + C
Integrate the equation cos(8*x + -7)	Let u = 8x + -7, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8x + -7 to get (1/8) * sin(8*x + -7). Finally, add the constant of integration C.	(1/8) * sin(8*x + -7) + C
Integrate the equation cos(3*x + 4)	Let u = 3x + 4, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3x + 4 to get (1/3) * sin(3*x + 4). Finally, add the constant of integration C.	(1/3) * sin(3*x + 4) + C
Integrate the equation cos(10*x + 6)	Let u = 10x + 6, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10x + 6 to get (1/10) * sin(10*x + 6). Finally, add the constant of integration C.	(1/10) * sin(10*x + 6) + C
Integrate the equation cos(4*x + -8)	Let u = 4x + -8, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4x + -8 to get (1/4) * sin(4*x + -8). Finally, add the constant of integration C.	(1/4) * sin(4*x + -8) + C
Integrate the equation cos(9*x + 9)	Let u = 9x + 9, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9x + 9 to get (1/9) * sin(9*x + 9). Finally, add the constant of integration C.	(1/9) * sin(9*x + 9) + C
Integrate the equation cos(7*x + -1)	Let u = 7x + -1, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7x + -1 to get (1/7) * sin(7*x + -1). Finally, add the constant of integration C.	(1/7) * sin(7*x + -1) + C
Integrate the equation cos(3*x + 8)	Let u = 3x + 8, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3x + 8 to get (1/3) * sin(3*x + 8). Finally, add the constant of integration C.	(1/3) * sin(3*x + 8) + C
Integrate the equation cos(9*x + 10)	Let u = 9x + 10, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9x + 10 to get (1/9) * sin(9*x + 10). Finally, add the constant of integration C.	(1/9) * sin(9*x + 10) + C
Integrate the equation cos(1*x + 5)	Let u = 1x + 5, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1x + 5 to get (1/1) * sin(1*x + 5). Finally, add the constant of integration C.	(1/1) * sin(1*x + 5) + C
Integrate the equation cos(3*x + -8)	Let u = 3x + -8, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3x + -8 to get (1/3) * sin(3*x + -8). Finally, add the constant of integration C.	(1/3) * sin(3*x + -8) + C
Integrate the equation cos(7*x + -2)	Let u = 7x + -2, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7x + -2 to get (1/7) * sin(7*x + -2). Finally, add the constant of integration C.	(1/7) * sin(7*x + -2) + C
Integrate the equation cos(1*x + -8)	Let u = 1x + -8, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1x + -8 to get (1/1) * sin(1*x + -8). Finally, add the constant of integration C.	(1/1) * sin(1*x + -8) + C
Integrate the equation cos(4*x + 7)	Let u = 4x + 7, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4x + 7 to get (1/4) * sin(4*x + 7). Finally, add the constant of integration C.	(1/4) * sin(4*x + 7) + C
Integrate the equation cos(5*x + 6)	Let u = 5x + 6, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5x + 6 to get (1/5) * sin(5*x + 6). Finally, add the constant of integration C.	(1/5) * sin(5*x + 6) + C
Integrate the equation cos(7*x + 10)	Let u = 7x + 10, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7x + 10 to get (1/7) * sin(7*x + 10). Finally, add the constant of integration C.	(1/7) * sin(7*x + 10) + C
Integrate the equation cos(2*x + -4)	Let u = 2x + -4, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2x + -4 to get (1/2) * sin(2*x + -4). Finally, add the constant of integration C.	(1/2) * sin(2*x + -4) + C
Integrate the equation cos(9*x + 10)	Let u = 9x + 10, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9x + 10 to get (1/9) * sin(9*x + 10). Finally, add the constant of integration C.	(1/9) * sin(9*x + 10) + C
Integrate the equation cos(6*x + 4)	Let u = 6x + 4, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + 4 to get (1/6) * sin(6*x + 4). Finally, add the constant of integration C.	(1/6) * sin(6*x + 4) + C
Integrate the equation cos(6*x + 5)	Let u = 6x + 5, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + 5 to get (1/6) * sin(6*x + 5). Finally, add the constant of integration C.	(1/6) * sin(6*x + 5) + C
Integrate the equation cos(10*x + -4)	Let u = 10x + -4, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10x + -4 to get (1/10) * sin(10*x + -4). Finally, add the constant of integration C.	(1/10) * sin(10*x + -4) + C
Integrate the equation cos(5*x + -8)	Let u = 5x + -8, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5x + -8 to get (1/5) * sin(5*x + -8). Finally, add the constant of integration C.	(1/5) * sin(5*x + -8) + C
Integrate the equation cos(8*x + -2)	Let u = 8x + -2, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8x + -2 to get (1/8) * sin(8*x + -2). Finally, add the constant of integration C.	(1/8) * sin(8*x + -2) + C
Integrate the equation cos(9*x + -7)	Let u = 9x + -7, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9x + -7 to get (1/9) * sin(9*x + -7). Finally, add the constant of integration C.	(1/9) * sin(9*x + -7) + C
Integrate the equation cos(5*x + 10)	Let u = 5x + 10, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5x + 10 to get (1/5) * sin(5*x + 10). Finally, add the constant of integration C.	(1/5) * sin(5*x + 10) + C
Integrate the equation cos(8*x + 10)	Let u = 8x + 10, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8x + 10 to get (1/8) * sin(8*x + 10). Finally, add the constant of integration C.	(1/8) * sin(8*x + 10) + C
Integrate the equation cos(1*x + -4)	Let u = 1x + -4, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1x + -4 to get (1/1) * sin(1*x + -4). Finally, add the constant of integration C.	(1/1) * sin(1*x + -4) + C
Integrate the equation cos(4*x + 7)	Let u = 4x + 7, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4x + 7 to get (1/4) * sin(4*x + 7). Finally, add the constant of integration C.	(1/4) * sin(4*x + 7) + C
Integrate the equation cos(10*x + 0)	Let u = 10x + 0, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10x + 0 to get (1/10) * sin(10*x + 0). Finally, add the constant of integration C.	(1/10) * sin(10*x + 0) + C
Integrate the equation cos(3*x + 1)	Let u = 3x + 1, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3x + 1 to get (1/3) * sin(3*x + 1). Finally, add the constant of integration C.	(1/3) * sin(3*x + 1) + C
Integrate the equation cos(4*x + -6)	Let u = 4x + -6, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4x + -6 to get (1/4) * sin(4*x + -6). Finally, add the constant of integration C.	(1/4) * sin(4*x + -6) + C
Integrate the equation cos(10*x + -2)	Let u = 10x + -2, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10x + -2 to get (1/10) * sin(10*x + -2). Finally, add the constant of integration C.	(1/10) * sin(10*x + -2) + C
Integrate the equation cos(3*x + -3)	Let u = 3x + -3, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3x + -3 to get (1/3) * sin(3*x + -3). Finally, add the constant of integration C.	(1/3) * sin(3*x + -3) + C
Integrate the equation cos(3*x + -2)	Let u = 3x + -2, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3x + -2 to get (1/3) * sin(3*x + -2). Finally, add the constant of integration C.	(1/3) * sin(3*x + -2) + C
Integrate the equation cos(10*x + -6)	Let u = 10x + -6, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10x + -6 to get (1/10) * sin(10*x + -6). Finally, add the constant of integration C.	(1/10) * sin(10*x + -6) + C
Integrate the equation cos(6*x + -6)	Let u = 6x + -6, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + -6 to get (1/6) * sin(6*x + -6). Finally, add the constant of integration C.	(1/6) * sin(6*x + -6) + C
Integrate the equation cos(7*x + 1)	Let u = 7x + 1, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7x + 1 to get (1/7) * sin(7*x + 1). Finally, add the constant of integration C.	(1/7) * sin(7*x + 1) + C
Integrate the equation cos(7*x + -4)	Let u = 7x + -4, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7x + -4 to get (1/7) * sin(7*x + -4). Finally, add the constant of integration C.	(1/7) * sin(7*x + -4) + C
Integrate the equation cos(4*x + -9)	Let u = 4x + -9, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4x + -9 to get (1/4) * sin(4*x + -9). Finally, add the constant of integration C.	(1/4) * sin(4*x + -9) + C
Integrate the equation cos(6*x + -2)	Let u = 6x + -2, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + -2 to get (1/6) * sin(6*x + -2). Finally, add the constant of integration C.	(1/6) * sin(6*x + -2) + C
Integrate the equation cos(3*x + -9)	Let u = 3x + -9, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3x + -9 to get (1/3) * sin(3*x + -9). Finally, add the constant of integration C.	(1/3) * sin(3*x + -9) + C
Integrate the equation cos(5*x + 0)	Let u = 5x + 0, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5x + 0 to get (1/5) * sin(5*x + 0). Finally, add the constant of integration C.	(1/5) * sin(5*x + 0) + C
Integrate the equation cos(2*x + 8)	Let u = 2x + 8, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2x + 8 to get (1/2) * sin(2*x + 8). Finally, add the constant of integration C.	(1/2) * sin(2*x + 8) + C
Integrate the equation cos(3*x + 2)	Let u = 3x + 2, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3x + 2 to get (1/3) * sin(3*x + 2). Finally, add the constant of integration C.	(1/3) * sin(3*x + 2) + C
Integrate the equation cos(8*x + 9)	Let u = 8x + 9, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8x + 9 to get (1/8) * sin(8*x + 9). Finally, add the constant of integration C.	(1/8) * sin(8*x + 9) + C
Integrate the equation cos(7*x + 0)	Let u = 7x + 0, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7x + 0 to get (1/7) * sin(7*x + 0). Finally, add the constant of integration C.	(1/7) * sin(7*x + 0) + C
Integrate the equation cos(1*x + -10)	Let u = 1x + -10, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1x + -10 to get (1/1) * sin(1*x + -10). Finally, add the constant of integration C.	(1/1) * sin(1*x + -10) + C
Integrate the equation cos(8*x + -6)	Let u = 8x + -6, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8x + -6 to get (1/8) * sin(8*x + -6). Finally, add the constant of integration C.	(1/8) * sin(8*x + -6) + C
Integrate the equation cos(6*x + 2)	Let u = 6x + 2, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + 2 to get (1/6) * sin(6*x + 2). Finally, add the constant of integration C.	(1/6) * sin(6*x + 2) + C
Integrate the equation cos(5*x + -3)	Let u = 5x + -3, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5x + -3 to get (1/5) * sin(5*x + -3). Finally, add the constant of integration C.	(1/5) * sin(5*x + -3) + C
Integrate the equation cos(6*x + -10)	Let u = 6x + -10, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + -10 to get (1/6) * sin(6*x + -10). Finally, add the constant of integration C.	(1/6) * sin(6*x + -10) + C
Integrate the equation cos(4*x + 6)	Let u = 4x + 6, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4x + 6 to get (1/4) * sin(4*x + 6). Finally, add the constant of integration C.	(1/4) * sin(4*x + 6) + C
Integrate the equation cos(5*x + 9)	Let u = 5x + 9, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5x + 9 to get (1/5) * sin(5*x + 9). Finally, add the constant of integration C.	(1/5) * sin(5*x + 9) + C
Integrate the equation cos(2*x + 10)	Let u = 2x + 10, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2x + 10 to get (1/2) * sin(2*x + 10). Finally, add the constant of integration C.	(1/2) * sin(2*x + 10) + C
Integrate the equation cos(9*x + -10)	Let u = 9x + -10, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9x + -10 to get (1/9) * sin(9*x + -10). Finally, add the constant of integration C.	(1/9) * sin(9*x + -10) + C
Integrate the equation cos(6*x + -1)	Let u = 6x + -1, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + -1 to get (1/6) * sin(6*x + -1). Finally, add the constant of integration C.	(1/6) * sin(6*x + -1) + C
Integrate the equation cos(6*x + 7)	Let u = 6x + 7, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + 7 to get (1/6) * sin(6*x + 7). Finally, add the constant of integration C.	(1/6) * sin(6*x + 7) + C
Integrate the equation cos(2*x + 7)	Let u = 2x + 7, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2x + 7 to get (1/2) * sin(2*x + 7). Finally, add the constant of integration C.	(1/2) * sin(2*x + 7) + C
Integrate the equation cos(10*x + 8)	Let u = 10x + 8, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10x + 8 to get (1/10) * sin(10*x + 8). Finally, add the constant of integration C.	(1/10) * sin(10*x + 8) + C
Integrate the equation cos(5*x + -1)	Let u = 5x + -1, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5x + -1 to get (1/5) * sin(5*x + -1). Finally, add the constant of integration C.	(1/5) * sin(5*x + -1) + C
Integrate the equation cos(10*x + -7)	Let u = 10x + -7, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10x + -7 to get (1/10) * sin(10*x + -7). Finally, add the constant of integration C.	(1/10) * sin(10*x + -7) + C
Integrate the equation cos(7*x + -6)	Let u = 7x + -6, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7x + -6 to get (1/7) * sin(7*x + -6). Finally, add the constant of integration C.	(1/7) * sin(7*x + -6) + C
Integrate the equation cos(9*x + -9)	Let u = 9x + -9, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9x + -9 to get (1/9) * sin(9*x + -9). Finally, add the constant of integration C.	(1/9) * sin(9*x + -9) + C
Integrate the equation cos(2*x + -8)	Let u = 2x + -8, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2x + -8 to get (1/2) * sin(2*x + -8). Finally, add the constant of integration C.	(1/2) * sin(2*x + -8) + C
Integrate the equation cos(5*x + 5)	Let u = 5x + 5, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5x + 5 to get (1/5) * sin(5*x + 5). Finally, add the constant of integration C.	(1/5) * sin(5*x + 5) + C
Integrate the equation cos(5*x + -10)	Let u = 5x + -10, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5x + -10 to get (1/5) * sin(5*x + -10). Finally, add the constant of integration C.	(1/5) * sin(5*x + -10) + C
Integrate the equation cos(6*x + 4)	Let u = 6x + 4, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + 4 to get (1/6) * sin(6*x + 4). Finally, add the constant of integration C.	(1/6) * sin(6*x + 4) + C
Integrate the equation cos(6*x + -10)	Let u = 6x + -10, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + -10 to get (1/6) * sin(6*x + -10). Finally, add the constant of integration C.	(1/6) * sin(6*x + -10) + C
Integrate the equation cos(3*x + 4)	Let u = 3x + 4, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3x + 4 to get (1/3) * sin(3*x + 4). Finally, add the constant of integration C.	(1/3) * sin(3*x + 4) + C
Integrate the equation cos(8*x + 10)	Let u = 8x + 10, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8x + 10 to get (1/8) * sin(8*x + 10). Finally, add the constant of integration C.	(1/8) * sin(8*x + 10) + C
Integrate the equation cos(9*x + 1)	Let u = 9x + 1, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9x + 1 to get (1/9) * sin(9*x + 1). Finally, add the constant of integration C.	(1/9) * sin(9*x + 1) + C
Integrate the equation cos(6*x + -4)	Let u = 6x + -4, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + -4 to get (1/6) * sin(6*x + -4). Finally, add the constant of integration C.	(1/6) * sin(6*x + -4) + C
Integrate the equation cos(1*x + -2)	Let u = 1x + -2, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1x + -2 to get (1/1) * sin(1*x + -2). Finally, add the constant of integration C.	(1/1) * sin(1*x + -2) + C
Integrate the equation cos(6*x + -7)	Let u = 6x + -7, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + -7 to get (1/6) * sin(6*x + -7). Finally, add the constant of integration C.	(1/6) * sin(6*x + -7) + C
Integrate the equation cos(7*x + 7)	Let u = 7x + 7, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7x + 7 to get (1/7) * sin(7*x + 7). Finally, add the constant of integration C.	(1/7) * sin(7*x + 7) + C
Integrate the equation cos(5*x + -9)	Let u = 5x + -9, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5x + -9 to get (1/5) * sin(5*x + -9). Finally, add the constant of integration C.	(1/5) * sin(5*x + -9) + C
Integrate the equation cos(6*x + -9)	Let u = 6x + -9, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + -9 to get (1/6) * sin(6*x + -9). Finally, add the constant of integration C.	(1/6) * sin(6*x + -9) + C
Integrate the equation cos(4*x + 9)	Let u = 4x + 9, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4x + 9 to get (1/4) * sin(4*x + 9). Finally, add the constant of integration C.	(1/4) * sin(4*x + 9) + C
Integrate the equation cos(7*x + 8)	Let u = 7x + 8, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7x + 8 to get (1/7) * sin(7*x + 8). Finally, add the constant of integration C.	(1/7) * sin(7*x + 8) + C
Integrate the equation cos(6*x + 4)	Let u = 6x + 4, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + 4 to get (1/6) * sin(6*x + 4). Finally, add the constant of integration C.	(1/6) * sin(6*x + 4) + C
Integrate the equation cos(1*x + -5)	Let u = 1x + -5, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1x + -5 to get (1/1) * sin(1*x + -5). Finally, add the constant of integration C.	(1/1) * sin(1*x + -5) + C
Integrate the equation cos(5*x + 5)	Let u = 5x + 5, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5x + 5 to get (1/5) * sin(5*x + 5). Finally, add the constant of integration C.	(1/5) * sin(5*x + 5) + C
Integrate the equation cos(8*x + -6)	Let u = 8x + -6, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8x + -6 to get (1/8) * sin(8*x + -6). Finally, add the constant of integration C.	(1/8) * sin(8*x + -6) + C
Integrate the equation cos(6*x + -4)	Let u = 6x + -4, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + -4 to get (1/6) * sin(6*x + -4). Finally, add the constant of integration C.	(1/6) * sin(6*x + -4) + C
Integrate the equation cos(1*x + -3)	Let u = 1x + -3, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1x + -3 to get (1/1) * sin(1*x + -3). Finally, add the constant of integration C.	(1/1) * sin(1*x + -3) + C
Integrate the equation cos(1*x + -6)	Let u = 1x + -6, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1x + -6 to get (1/1) * sin(1*x + -6). Finally, add the constant of integration C.	(1/1) * sin(1*x + -6) + C
Integrate the equation cos(2*x + -4)	Let u = 2x + -4, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2x + -4 to get (1/2) * sin(2*x + -4). Finally, add the constant of integration C.	(1/2) * sin(2*x + -4) + C
Integrate the equation cos(4*x + -10)	Let u = 4x + -10, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4x + -10 to get (1/4) * sin(4*x + -10). Finally, add the constant of integration C.	(1/4) * sin(4*x + -10) + C
Integrate the equation cos(6*x + -2)	Let u = 6x + -2, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + -2 to get (1/6) * sin(6*x + -2). Finally, add the constant of integration C.	(1/6) * sin(6*x + -2) + C
Integrate the equation cos(6*x + 3)	Let u = 6x + 3, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + 3 to get (1/6) * sin(6*x + 3). Finally, add the constant of integration C.	(1/6) * sin(6*x + 3) + C
Integrate the equation cos(8*x + 4)	Let u = 8x + 4, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8x + 4 to get (1/8) * sin(8*x + 4). Finally, add the constant of integration C.	(1/8) * sin(8*x + 4) + C
Integrate the equation cos(7*x + 7)	Let u = 7x + 7, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7x + 7 to get (1/7) * sin(7*x + 7). Finally, add the constant of integration C.	(1/7) * sin(7*x + 7) + C
Integrate the equation cos(9*x + 10)	Let u = 9x + 10, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9x + 10 to get (1/9) * sin(9*x + 10). Finally, add the constant of integration C.	(1/9) * sin(9*x + 10) + C
Integrate the equation cos(5*x + -8)	Let u = 5x + -8, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5x + -8 to get (1/5) * sin(5*x + -8). Finally, add the constant of integration C.	(1/5) * sin(5*x + -8) + C
Integrate the equation cos(6*x + -10)	Let u = 6x + -10, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6x + -10 to get (1/6) * sin(6*x + -10). Finally, add the constant of integration C.	(1/6) * sin(6*x + -10) + C

Integrate the equation cos(1*x + 4)

Let u = 1*x + 4, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1*x + 4 to get (1/1) * sin(1*x + 4). Finally, add the constant of integration C.

(1/1) * sin(1*x + 4) + C

Integrate the equation cos(7*x + 8)

Let u = 7*x + 8, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7*x + 8 to get (1/7) * sin(7*x + 8). Finally, add the constant of integration C.

(1/7) * sin(7*x + 8) + C

Integrate the equation cos(5*x + 3)

Let u = 5*x + 3, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5*x + 3 to get (1/5) * sin(5*x + 3). Finally, add the constant of integration C.

(1/5) * sin(5*x + 3) + C

Integrate the equation cos(9*x + 0)

Let u = 9*x + 0, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9*x + 0 to get (1/9) * sin(9*x + 0). Finally, add the constant of integration C.

(1/9) * sin(9*x + 0) + C

Integrate the equation cos(7*x + -2)

Let u = 7*x + -2, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7*x + -2 to get (1/7) * sin(7*x + -2). Finally, add the constant of integration C.

(1/7) * sin(7*x + -2) + C

Integrate the equation cos(2*x + -8)

Let u = 2*x + -8, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2*x + -8 to get (1/2) * sin(2*x + -8). Finally, add the constant of integration C.

(1/2) * sin(2*x + -8) + C

Integrate the equation cos(8*x + -7)

Let u = 8*x + -7, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8*x + -7 to get (1/8) * sin(8*x + -7). Finally, add the constant of integration C.

(1/8) * sin(8*x + -7) + C

Integrate the equation cos(3*x + 4)

Let u = 3*x + 4, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3*x + 4 to get (1/3) * sin(3*x + 4). Finally, add the constant of integration C.

(1/3) * sin(3*x + 4) + C

Integrate the equation cos(10*x + 6)

Let u = 10*x + 6, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10*x + 6 to get (1/10) * sin(10*x + 6). Finally, add the constant of integration C.

(1/10) * sin(10*x + 6) + C

Integrate the equation cos(4*x + -8)

Let u = 4*x + -8, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4*x + -8 to get (1/4) * sin(4*x + -8). Finally, add the constant of integration C.

(1/4) * sin(4*x + -8) + C

Integrate the equation cos(9*x + 9)

Let u = 9*x + 9, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9*x + 9 to get (1/9) * sin(9*x + 9). Finally, add the constant of integration C.

(1/9) * sin(9*x + 9) + C

Integrate the equation cos(7*x + -1)

Let u = 7*x + -1, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7*x + -1 to get (1/7) * sin(7*x + -1). Finally, add the constant of integration C.

(1/7) * sin(7*x + -1) + C

Integrate the equation cos(3*x + 8)

Let u = 3*x + 8, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3*x + 8 to get (1/3) * sin(3*x + 8). Finally, add the constant of integration C.

(1/3) * sin(3*x + 8) + C

Integrate the equation cos(9*x + 10)

Let u = 9*x + 10, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9*x + 10 to get (1/9) * sin(9*x + 10). Finally, add the constant of integration C.

(1/9) * sin(9*x + 10) + C

Integrate the equation cos(1*x + 5)

Let u = 1*x + 5, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1*x + 5 to get (1/1) * sin(1*x + 5). Finally, add the constant of integration C.

(1/1) * sin(1*x + 5) + C

Integrate the equation cos(3*x + -8)

Let u = 3*x + -8, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3*x + -8 to get (1/3) * sin(3*x + -8). Finally, add the constant of integration C.

(1/3) * sin(3*x + -8) + C

Integrate the equation cos(7*x + -2)

Let u = 7*x + -2, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7*x + -2 to get (1/7) * sin(7*x + -2). Finally, add the constant of integration C.

(1/7) * sin(7*x + -2) + C

Integrate the equation cos(1*x + -8)

Let u = 1*x + -8, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1*x + -8 to get (1/1) * sin(1*x + -8). Finally, add the constant of integration C.

(1/1) * sin(1*x + -8) + C

Integrate the equation cos(4*x + 7)

Let u = 4*x + 7, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4*x + 7 to get (1/4) * sin(4*x + 7). Finally, add the constant of integration C.

(1/4) * sin(4*x + 7) + C

Integrate the equation cos(5*x + 6)

Let u = 5*x + 6, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5*x + 6 to get (1/5) * sin(5*x + 6). Finally, add the constant of integration C.

(1/5) * sin(5*x + 6) + C

Integrate the equation cos(7*x + 10)

Let u = 7*x + 10, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7*x + 10 to get (1/7) * sin(7*x + 10). Finally, add the constant of integration C.

(1/7) * sin(7*x + 10) + C

Integrate the equation cos(2*x + -4)

Let u = 2*x + -4, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2*x + -4 to get (1/2) * sin(2*x + -4). Finally, add the constant of integration C.

(1/2) * sin(2*x + -4) + C

Integrate the equation cos(9*x + 10)

Let u = 9*x + 10, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9*x + 10 to get (1/9) * sin(9*x + 10). Finally, add the constant of integration C.

(1/9) * sin(9*x + 10) + C

Integrate the equation cos(6*x + 4)

Let u = 6*x + 4, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + 4 to get (1/6) * sin(6*x + 4). Finally, add the constant of integration C.

(1/6) * sin(6*x + 4) + C

Integrate the equation cos(6*x + 5)

Let u = 6*x + 5, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + 5 to get (1/6) * sin(6*x + 5). Finally, add the constant of integration C.

(1/6) * sin(6*x + 5) + C

Integrate the equation cos(10*x + -4)

Let u = 10*x + -4, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10*x + -4 to get (1/10) * sin(10*x + -4). Finally, add the constant of integration C.

(1/10) * sin(10*x + -4) + C

Integrate the equation cos(5*x + -8)

Let u = 5*x + -8, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5*x + -8 to get (1/5) * sin(5*x + -8). Finally, add the constant of integration C.

(1/5) * sin(5*x + -8) + C

Integrate the equation cos(8*x + -2)

Let u = 8*x + -2, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8*x + -2 to get (1/8) * sin(8*x + -2). Finally, add the constant of integration C.

(1/8) * sin(8*x + -2) + C

Integrate the equation cos(9*x + -7)

Let u = 9*x + -7, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9*x + -7 to get (1/9) * sin(9*x + -7). Finally, add the constant of integration C.

(1/9) * sin(9*x + -7) + C

Integrate the equation cos(5*x + 10)

Let u = 5*x + 10, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5*x + 10 to get (1/5) * sin(5*x + 10). Finally, add the constant of integration C.

(1/5) * sin(5*x + 10) + C

Integrate the equation cos(8*x + 10)

Let u = 8*x + 10, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8*x + 10 to get (1/8) * sin(8*x + 10). Finally, add the constant of integration C.

(1/8) * sin(8*x + 10) + C

Integrate the equation cos(1*x + -4)

Let u = 1*x + -4, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1*x + -4 to get (1/1) * sin(1*x + -4). Finally, add the constant of integration C.

(1/1) * sin(1*x + -4) + C

Integrate the equation cos(4*x + 7)

Let u = 4*x + 7, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4*x + 7 to get (1/4) * sin(4*x + 7). Finally, add the constant of integration C.

(1/4) * sin(4*x + 7) + C

Integrate the equation cos(10*x + 0)

Let u = 10*x + 0, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10*x + 0 to get (1/10) * sin(10*x + 0). Finally, add the constant of integration C.

(1/10) * sin(10*x + 0) + C

Integrate the equation cos(3*x + 1)

Let u = 3*x + 1, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3*x + 1 to get (1/3) * sin(3*x + 1). Finally, add the constant of integration C.

(1/3) * sin(3*x + 1) + C

Integrate the equation cos(4*x + -6)

Let u = 4*x + -6, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4*x + -6 to get (1/4) * sin(4*x + -6). Finally, add the constant of integration C.

(1/4) * sin(4*x + -6) + C

Integrate the equation cos(10*x + -2)

Let u = 10*x + -2, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10*x + -2 to get (1/10) * sin(10*x + -2). Finally, add the constant of integration C.

(1/10) * sin(10*x + -2) + C

Integrate the equation cos(3*x + -3)

Let u = 3*x + -3, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3*x + -3 to get (1/3) * sin(3*x + -3). Finally, add the constant of integration C.

(1/3) * sin(3*x + -3) + C

Integrate the equation cos(3*x + -2)

Let u = 3*x + -2, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3*x + -2 to get (1/3) * sin(3*x + -2). Finally, add the constant of integration C.

(1/3) * sin(3*x + -2) + C

Integrate the equation cos(10*x + -6)

Let u = 10*x + -6, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10*x + -6 to get (1/10) * sin(10*x + -6). Finally, add the constant of integration C.

(1/10) * sin(10*x + -6) + C

Integrate the equation cos(6*x + -6)

Let u = 6*x + -6, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + -6 to get (1/6) * sin(6*x + -6). Finally, add the constant of integration C.

(1/6) * sin(6*x + -6) + C

Integrate the equation cos(7*x + 1)

Let u = 7*x + 1, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7*x + 1 to get (1/7) * sin(7*x + 1). Finally, add the constant of integration C.

(1/7) * sin(7*x + 1) + C

Integrate the equation cos(7*x + -4)

Let u = 7*x + -4, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7*x + -4 to get (1/7) * sin(7*x + -4). Finally, add the constant of integration C.

(1/7) * sin(7*x + -4) + C

Integrate the equation cos(4*x + -9)

Let u = 4*x + -9, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4*x + -9 to get (1/4) * sin(4*x + -9). Finally, add the constant of integration C.

(1/4) * sin(4*x + -9) + C

Integrate the equation cos(6*x + -2)

Let u = 6*x + -2, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + -2 to get (1/6) * sin(6*x + -2). Finally, add the constant of integration C.

(1/6) * sin(6*x + -2) + C

Integrate the equation cos(3*x + -9)

Let u = 3*x + -9, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3*x + -9 to get (1/3) * sin(3*x + -9). Finally, add the constant of integration C.

(1/3) * sin(3*x + -9) + C

Integrate the equation cos(5*x + 0)

Let u = 5*x + 0, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5*x + 0 to get (1/5) * sin(5*x + 0). Finally, add the constant of integration C.

(1/5) * sin(5*x + 0) + C

Integrate the equation cos(2*x + 8)

Let u = 2*x + 8, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2*x + 8 to get (1/2) * sin(2*x + 8). Finally, add the constant of integration C.

(1/2) * sin(2*x + 8) + C

Integrate the equation cos(3*x + 2)

Let u = 3*x + 2, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3*x + 2 to get (1/3) * sin(3*x + 2). Finally, add the constant of integration C.

(1/3) * sin(3*x + 2) + C

Integrate the equation cos(8*x + 9)

Let u = 8*x + 9, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8*x + 9 to get (1/8) * sin(8*x + 9). Finally, add the constant of integration C.

(1/8) * sin(8*x + 9) + C

Integrate the equation cos(7*x + 0)

Let u = 7*x + 0, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7*x + 0 to get (1/7) * sin(7*x + 0). Finally, add the constant of integration C.

(1/7) * sin(7*x + 0) + C

Integrate the equation cos(1*x + -10)

Let u = 1*x + -10, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1*x + -10 to get (1/1) * sin(1*x + -10). Finally, add the constant of integration C.

(1/1) * sin(1*x + -10) + C

Integrate the equation cos(8*x + -6)

Let u = 8*x + -6, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8*x + -6 to get (1/8) * sin(8*x + -6). Finally, add the constant of integration C.

(1/8) * sin(8*x + -6) + C

Integrate the equation cos(6*x + 2)

Let u = 6*x + 2, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + 2 to get (1/6) * sin(6*x + 2). Finally, add the constant of integration C.

(1/6) * sin(6*x + 2) + C

Integrate the equation cos(5*x + -3)

Let u = 5*x + -3, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5*x + -3 to get (1/5) * sin(5*x + -3). Finally, add the constant of integration C.

(1/5) * sin(5*x + -3) + C

Integrate the equation cos(6*x + -10)

Let u = 6*x + -10, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + -10 to get (1/6) * sin(6*x + -10). Finally, add the constant of integration C.

(1/6) * sin(6*x + -10) + C

Integrate the equation cos(4*x + 6)

Let u = 4*x + 6, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4*x + 6 to get (1/4) * sin(4*x + 6). Finally, add the constant of integration C.

(1/4) * sin(4*x + 6) + C

Integrate the equation cos(5*x + 9)

Let u = 5*x + 9, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5*x + 9 to get (1/5) * sin(5*x + 9). Finally, add the constant of integration C.

(1/5) * sin(5*x + 9) + C

Integrate the equation cos(2*x + 10)

Let u = 2*x + 10, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2*x + 10 to get (1/2) * sin(2*x + 10). Finally, add the constant of integration C.

(1/2) * sin(2*x + 10) + C

Integrate the equation cos(9*x + -10)

Let u = 9*x + -10, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9*x + -10 to get (1/9) * sin(9*x + -10). Finally, add the constant of integration C.

(1/9) * sin(9*x + -10) + C

Integrate the equation cos(6*x + -1)

Let u = 6*x + -1, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + -1 to get (1/6) * sin(6*x + -1). Finally, add the constant of integration C.

(1/6) * sin(6*x + -1) + C

Integrate the equation cos(6*x + 7)

Let u = 6*x + 7, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + 7 to get (1/6) * sin(6*x + 7). Finally, add the constant of integration C.

(1/6) * sin(6*x + 7) + C

Integrate the equation cos(2*x + 7)

Let u = 2*x + 7, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2*x + 7 to get (1/2) * sin(2*x + 7). Finally, add the constant of integration C.

(1/2) * sin(2*x + 7) + C

Integrate the equation cos(10*x + 8)

Let u = 10*x + 8, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10*x + 8 to get (1/10) * sin(10*x + 8). Finally, add the constant of integration C.

(1/10) * sin(10*x + 8) + C

Integrate the equation cos(5*x + -1)

Let u = 5*x + -1, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5*x + -1 to get (1/5) * sin(5*x + -1). Finally, add the constant of integration C.

(1/5) * sin(5*x + -1) + C

Integrate the equation cos(10*x + -7)

Let u = 10*x + -7, so du/dx = 10 and dx = du/10. Rewrite the integral as (1/10) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 10*x + -7 to get (1/10) * sin(10*x + -7). Finally, add the constant of integration C.

(1/10) * sin(10*x + -7) + C

Integrate the equation cos(7*x + -6)

Let u = 7*x + -6, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7*x + -6 to get (1/7) * sin(7*x + -6). Finally, add the constant of integration C.

(1/7) * sin(7*x + -6) + C

Integrate the equation cos(9*x + -9)

Let u = 9*x + -9, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9*x + -9 to get (1/9) * sin(9*x + -9). Finally, add the constant of integration C.

(1/9) * sin(9*x + -9) + C

Integrate the equation cos(2*x + -8)

Let u = 2*x + -8, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2*x + -8 to get (1/2) * sin(2*x + -8). Finally, add the constant of integration C.

(1/2) * sin(2*x + -8) + C

Integrate the equation cos(5*x + 5)

Let u = 5*x + 5, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5*x + 5 to get (1/5) * sin(5*x + 5). Finally, add the constant of integration C.

(1/5) * sin(5*x + 5) + C

Integrate the equation cos(5*x + -10)

Let u = 5*x + -10, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5*x + -10 to get (1/5) * sin(5*x + -10). Finally, add the constant of integration C.

(1/5) * sin(5*x + -10) + C

Integrate the equation cos(6*x + 4)

Let u = 6*x + 4, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + 4 to get (1/6) * sin(6*x + 4). Finally, add the constant of integration C.

(1/6) * sin(6*x + 4) + C

Integrate the equation cos(6*x + -10)

Let u = 6*x + -10, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + -10 to get (1/6) * sin(6*x + -10). Finally, add the constant of integration C.

(1/6) * sin(6*x + -10) + C

Integrate the equation cos(3*x + 4)

Let u = 3*x + 4, so du/dx = 3 and dx = du/3. Rewrite the integral as (1/3) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 3*x + 4 to get (1/3) * sin(3*x + 4). Finally, add the constant of integration C.

(1/3) * sin(3*x + 4) + C

Integrate the equation cos(8*x + 10)

Let u = 8*x + 10, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8*x + 10 to get (1/8) * sin(8*x + 10). Finally, add the constant of integration C.

(1/8) * sin(8*x + 10) + C

Integrate the equation cos(9*x + 1)

Let u = 9*x + 1, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9*x + 1 to get (1/9) * sin(9*x + 1). Finally, add the constant of integration C.

(1/9) * sin(9*x + 1) + C

Integrate the equation cos(6*x + -4)

Let u = 6*x + -4, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + -4 to get (1/6) * sin(6*x + -4). Finally, add the constant of integration C.

(1/6) * sin(6*x + -4) + C

Integrate the equation cos(1*x + -2)

Let u = 1*x + -2, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1*x + -2 to get (1/1) * sin(1*x + -2). Finally, add the constant of integration C.

(1/1) * sin(1*x + -2) + C

Integrate the equation cos(6*x + -7)

Let u = 6*x + -7, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + -7 to get (1/6) * sin(6*x + -7). Finally, add the constant of integration C.

(1/6) * sin(6*x + -7) + C

Integrate the equation cos(7*x + 7)

Let u = 7*x + 7, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7*x + 7 to get (1/7) * sin(7*x + 7). Finally, add the constant of integration C.

(1/7) * sin(7*x + 7) + C

Integrate the equation cos(5*x + -9)

Let u = 5*x + -9, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5*x + -9 to get (1/5) * sin(5*x + -9). Finally, add the constant of integration C.

(1/5) * sin(5*x + -9) + C

Integrate the equation cos(6*x + -9)

Let u = 6*x + -9, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + -9 to get (1/6) * sin(6*x + -9). Finally, add the constant of integration C.

(1/6) * sin(6*x + -9) + C

Integrate the equation cos(4*x + 9)

Let u = 4*x + 9, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4*x + 9 to get (1/4) * sin(4*x + 9). Finally, add the constant of integration C.

(1/4) * sin(4*x + 9) + C

Integrate the equation cos(7*x + 8)

Let u = 7*x + 8, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7*x + 8 to get (1/7) * sin(7*x + 8). Finally, add the constant of integration C.

(1/7) * sin(7*x + 8) + C

Integrate the equation cos(6*x + 4)

Let u = 6*x + 4, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + 4 to get (1/6) * sin(6*x + 4). Finally, add the constant of integration C.

(1/6) * sin(6*x + 4) + C

Integrate the equation cos(1*x + -5)

Let u = 1*x + -5, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1*x + -5 to get (1/1) * sin(1*x + -5). Finally, add the constant of integration C.

(1/1) * sin(1*x + -5) + C

Integrate the equation cos(5*x + 5)

Let u = 5*x + 5, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5*x + 5 to get (1/5) * sin(5*x + 5). Finally, add the constant of integration C.

(1/5) * sin(5*x + 5) + C

Integrate the equation cos(8*x + -6)

Let u = 8*x + -6, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8*x + -6 to get (1/8) * sin(8*x + -6). Finally, add the constant of integration C.

(1/8) * sin(8*x + -6) + C

Integrate the equation cos(6*x + -4)

Let u = 6*x + -4, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + -4 to get (1/6) * sin(6*x + -4). Finally, add the constant of integration C.

(1/6) * sin(6*x + -4) + C

Integrate the equation cos(1*x + -3)

Let u = 1*x + -3, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1*x + -3 to get (1/1) * sin(1*x + -3). Finally, add the constant of integration C.

(1/1) * sin(1*x + -3) + C

Integrate the equation cos(1*x + -6)

Let u = 1*x + -6, so du/dx = 1 and dx = du/1. Rewrite the integral as (1/1) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 1*x + -6 to get (1/1) * sin(1*x + -6). Finally, add the constant of integration C.

(1/1) * sin(1*x + -6) + C

Integrate the equation cos(2*x + -4)

Let u = 2*x + -4, so du/dx = 2 and dx = du/2. Rewrite the integral as (1/2) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 2*x + -4 to get (1/2) * sin(2*x + -4). Finally, add the constant of integration C.

(1/2) * sin(2*x + -4) + C

Integrate the equation cos(4*x + -10)

Let u = 4*x + -10, so du/dx = 4 and dx = du/4. Rewrite the integral as (1/4) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 4*x + -10 to get (1/4) * sin(4*x + -10). Finally, add the constant of integration C.

(1/4) * sin(4*x + -10) + C

Integrate the equation cos(6*x + -2)

Let u = 6*x + -2, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + -2 to get (1/6) * sin(6*x + -2). Finally, add the constant of integration C.

(1/6) * sin(6*x + -2) + C

Integrate the equation cos(6*x + 3)

Let u = 6*x + 3, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + 3 to get (1/6) * sin(6*x + 3). Finally, add the constant of integration C.

(1/6) * sin(6*x + 3) + C

Integrate the equation cos(8*x + 4)

Let u = 8*x + 4, so du/dx = 8 and dx = du/8. Rewrite the integral as (1/8) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 8*x + 4 to get (1/8) * sin(8*x + 4). Finally, add the constant of integration C.

(1/8) * sin(8*x + 4) + C

Integrate the equation cos(7*x + 7)

Let u = 7*x + 7, so du/dx = 7 and dx = du/7. Rewrite the integral as (1/7) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 7*x + 7 to get (1/7) * sin(7*x + 7). Finally, add the constant of integration C.

(1/7) * sin(7*x + 7) + C

Integrate the equation cos(9*x + 10)

Let u = 9*x + 10, so du/dx = 9 and dx = du/9. Rewrite the integral as (1/9) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 9*x + 10 to get (1/9) * sin(9*x + 10). Finally, add the constant of integration C.

(1/9) * sin(9*x + 10) + C

Integrate the equation cos(5*x + -8)

Let u = 5*x + -8, so du/dx = 5 and dx = du/5. Rewrite the integral as (1/5) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 5*x + -8 to get (1/5) * sin(5*x + -8). Finally, add the constant of integration C.

(1/5) * sin(5*x + -8) + C

Integrate the equation cos(6*x + -10)

Let u = 6*x + -10, so du/dx = 6 and dx = du/6. Rewrite the integral as (1/6) cos(u) du. The integral of cos(u) is sin(u). Substitute back u = 6*x + -10 to get (1/6) * sin(6*x + -10). Finally, add the constant of integration C.

(1/6) * sin(6*x + -10) + C