Answer
-cot(x) -x +C
Work Step by Step
We find:
$cot^{2}x$=$\frac{cos^{2}x}{sin^{2}x}$=$\frac{1-sin^{2}x}{sin^{2}x}$=$csc^{2}x$-1
$\int$$cot^{2}x$
=$\int$($csc^{2}x$-1)dx
=$\int$$csc^{2}x$dx-$\int$1dx
$\int$$csc^{2}x$dx=-cot(x)+$C_{1}$ $\int$1dx=x+$C_{2}$
So the expression= -cot(x) -x +C
