$\int \frac{x cos x}{{(x sin x + cos x)}^{2}} d x .$

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Solution

$\int \frac{x cos x}{{(x sin x + cos x)}^{2}} d x$

$u = x sin x + cos x$

$d u = x cos x . d x$

$\int \frac{1}{u^{2}} d u$

$= \frac{- 1}{u} + c$

$= \frac{- 1}{x sin x + cos x} + c$

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