∫ x^2 cos x dx=x^2∫cos x ∫ 2x ∫cos x dx dx =x^2sin x ∫ 2xsin x dx =x^2sin x+2xcos x+∫ 2cos x dx =x^2sin x+2xcos x+sin x ...

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Integration by Parts

Solve ∫ x ...

Question

Solve $\int x^{2} cos x d x$

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Solution

$\int x^{2} cos x d x = x^{2} \int cos x - \int 2 x \int cos x d x d x$
$= x^{2} sin x - \int 2 x sin x d x$
$= x^{2} sin x + 2 x cos x + \int 2 cos x d x$
$= x^{2} sin x + 2 x cos x + sin x$

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