Answer
$-2\cot\left(\frac{x}{2}\right)+C$
Work Step by Step
$\int\csc^2\left({\frac{x}{2}}\right)dx$
$u=\frac{x}{2}\hspace{8mm}du=\frac{1}{2}dx\hspace{8mm}dx=2du$
$\int\csc^2\left({\frac{x}{2}}\right)dx=\int2\csc^2{u}du=2\int\csc^2{u}du$
$2(-\cot{u})+C=-2\cot\left(\frac{x}{2}\right)+C$
