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Step-by-step solution of ∫x sin x dx using integration by parts

Integration by parts formula and example: ∫x sin x dx = -x cos x + sin x + C

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Show Answer Key & Explanations Step-by-step solution for: Calculus - Integration by Parts (solutions, examples, videos)

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- The integral ∫x sin x dx is solved using integration by parts, with u = x and dv = sin x dx.
- Then du = dx and v = -cos x.
- Applying the formula ∫u dv = uv - ∫v du gives x(-cos x) - ∫(-cos x) dx.
- Simplifying yields -x cos x + ∫cos x dx.
- The integral of cos x is sin x, so the result is -x cos x + sin x + C.

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