Question

$\int \frac{1}{\sin x{\cos }^{2}x}dx=$

Answer 1

Consider the following integral.

$\underset{}{\overset{}{\int }}\frac{1}{\sin x{\cos }^{2}x}dx$

$=\underset{}{\overset{}{\int }}\frac{1+{\tan }^{2}x}{\sin x}dx$

$=\underset{}{\overset{}{\int }}(\sec x\tan xdx+cscxdx)$

$=\int \sec x\tan xdx+\int \csc xdx$

$=\sec x-\ln (\csc x+\cot x)$

Hence, this is the correct answer.