Question

Solve ${\int }^{}\frac{x\cos x}{{\left(x\sin x+\cos x\right)}^2}dx$

Answer 1

$\int \frac{x\cos x}{{\left(x\sin x+\cos x\right)}^2}dx$

$putx\sin x+\cos x=u$

$dx=\frac{1}{x\cos x}du$

$\int \frac{du}{u^2}$

$-\frac{1}{4}+C$

$\frac{1}{x\sin x+\cos x}+C$