Question

$\frac{1}{sinxco{s}^{3}x}$

Answer 1

Consider the given function:

$\int \frac{1}{\sin x{\cos }^{3}x}$

$u=\cos x$

$du=-\sin xdx$

$-u=\sin xdx$

$=\int \frac{1}{u^3}.(-dv)$

$=-\int \frac{1}{u^3}.du$

$=-\frac{u^4}{4}=-\frac{{\cos }^4\left(x\right)}{4}+c$

Hence this is the answer.