Hint in integration $\int\frac{x^{2}}{\left(x\cos x-\sin x \right )\left( x\sin x+\cos x \right )}\,\mathrm{d}x$ In the following integration 
$$\int \frac{x^{2}}{\left ( x\cos x-\sin x \right )\left ( x\sin x+\cos x \right )}\, \mathrm{d}x$$
I tried alot. But does not get any proper start.
Can anybody provide me a hint.

Hint. One may observe the following trick
$$
\begin{align}
\frac{x^2}{(x \cos x-\sin x)(x\sin x+\cos x)}&=\frac{x\cos x(x \cos x-\sin x)+x\sin x(x\sin x+\cos x)}{(x \cos x-\sin x)(x\sin x+\cos x)}
\\\\&=\frac{x\cos x}{x\sin x+\cos x}+\frac{x \sin x}{x \cos x-\sin x}
\\\\&=\frac{(x\sin x+\cos x)'}{(x\sin x+\cos x)}-\frac{(x \cos x-\sin x)'}{(x \cos x-\sin x)}
\end{align}
$$ then one may conclude.
