Integrate the function $x sin x$

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Solution

$\int x sin x d x$
Using by parts,
$= x \int sin x d x - \int {(\frac{d}{d x} x) \int sin x d x} d x$
$= x (- cos x) - \int 1 \cdot (- cos x) d x$
$= - x cos x + sin x + C$

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