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Solve differential equation

y'' + y = 0

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Step-by-Step Solutions

Compute: ∫x sin(x) dx

Step 1: Integration by parts

∫u dv = uv - ∫v du

Step 2: Choose u and dv

Let u = x, dv = sin(x) dx

Step 3: Compute derivatives/integrals

du = dx, v = -cos(x)

Step 4: Apply integration by parts

∫x sin(x) dx = -x cos(x) - ∫-cos(x) dx

Step 5: Simplify

∫x sin(x) dx = -x cos(x) + ∫cos(x) dx
∫x sin(x) dx = -x cos(x) + sin(x) + C

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