<s>[INST] How to integrate this : $\int \frac{x^2+\cos^2 x}{1+x^2}\csc^2xdx$ How to integrate : 
$\int \frac{x^2+\cos^2x}{1+x^2}\csc^2xdx$ 
I am not getting any clue how to move further, request you to please provide hint, will be of great help. 
Thanks..
 [/INST] Let
$$\begin{align}
f(x) &= \frac{x^2+\cos^2x}{1+x^2} \csc^2x \\
&= \frac{x^2+ 1- \sin^2x}{1+x^2} \cdot \frac{1}{\sin^2x}\\
&= \frac{1}{\sin^2x} - \frac{1}{1+x^2}.
\end{align}$$
These two terms can be integrated easily.
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