Question

$\int {\cot }^{2}xdx=$

Answer 1

Consider the following integral.

$I=\underset{}{\overset{}{\int }}{\cot }^{2}xdx$

$=\underset{}{\overset{}{\int }}({\csc }^{2}x-1)dx$

$=\underset{}{\overset{}{\int }}\left({\csc }^{2}x\right)-\underset{}{\overset{}{\int }}1dx$

$=-\tan x-x+C$

Hence, This is the required answer.