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Solve ∫x²·sin(x) dx using integration by parts

Using integration by parts: ∫u dv = uv − ∫v du

Let u = x², dv = sin(x)dx

Then du = 2x dx, v = −cos(x)

= −x²cos(x) + 2∫x·cos(x) dx

Applying integration by parts again…

= −x²cos(x) + 2x·sin(x) + 2cos(x) + C

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