$\int \frac{x^2}{{\left(x\cos x-\sin x\right)}^2}dx=$_______________

$-\int \frac{-x\sin x}{{\left[x\cos x-\sin x\right]}^2}.\left(\frac{x}{\sin x}\right)dx$

And use integration by parts.

$-\left(\left(\frac{-1}{x\cos x-\sin x}\right)\frac{x}{\sin x}-\int \frac{\sin x-x\cos x}{{\sin }^{2}x}.\left(\frac{-1}{x\cos x-\sin x}\right)dx\right)$

$\frac{x\cos ecx}{x\cos x-\sin x}+\int \cos e{c}^{2}xdx+c$

$-\cot x+\frac{x\cos ecx}{x\cos x-\sin x}+c$