Evaluate the integrals $\int \sin{x} \cot^2{x} \,dx$ and $\int \cos{x} \cot^2{x} \,dx$. Can you please show how to evaluate the integrals $$\int \sin{x} \cot^2{x} \,dx$$ and $$\int \cos{x} \cot^2{x} \,dx.$$
I know that $\cot x=\dfrac{\cos x}{\sin x}$, which can simplify the integrands a bit. 
$$\sin x\cot^2x = \frac{\cos^2x}{\sin x}\\
\cos x\cot^2x = \frac{\cos^3x}{\sin^2 x}$$
But I still do not know where to continue from there.

Hint :
\begin{align}
\int\sin x\cot^2x\ dx&=\int\sin x\cdot\frac{\cos^2x}{\sin^2x}\ dx\\
&=\int\frac{\cos^2x}{\sin x}\ dx\\
&=\int\frac{1-\sin^2x}{\sin x}\ dx\\
&=\int \frac1{\sin x}\ dx-\int\sin x\ dx\\
&=\color{red}{\int \frac{\sin x}{1-\cos^2 x}\ dx}-\int\sin x\ dx\tag1
\end{align}
and
\begin{align}
\int\cos x\cot^2x\ dx&=\int\cos x\cdot\frac{\cos^2x}{\sin^2x}\ dx\\
&=\int\cos x\cdot\frac{1-\sin^2x}{\sin^2x}\ dx\tag2
\end{align}
For $(1)$ take substitution $\color{red}{u=\cos x}$ and for $(2)$ take substitution $v=\sin x$.
