Ok I am not sure if I am getting this right or not. My answer is slightly different to an answer I am getting from a symbolic calculator.

The question asks to evaluate

$\displaystyle \int \cot{x} \csc^{2}{x}dx$

So I substituted

$\displaystyle u=\cot{x} $

and

$\displaystyle du=-\csc^{2}xdx$

or

$\displaystyle -du=csc^{2}xdx$

so

$\displaystyle \int \cot{x} \csc^{2}xdx = \int-udu$

$\displaystyle =\frac{-u^{2}}{2}+C$

$\displaystyle =\frac{-cot^{2}x}{2}+C$

But the answer the calculator gives me is

$\displaystyle \frac{-csc^{2}x}{2}+C$

Can someone point out where I might have gone wrong. Thanks!