- #1

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## Homework Statement

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

## Homework Equations

## The Attempt at a Solution

Factoring out ##\cos x## from the denominator, the integral transforms to

[tex]\int \sec^2x \left(\frac{x}{x-\tan x}\right)^2dx[/tex]

Substituting ##\tan x=t##, ##\sec^2 xdx=dt##

[tex]\int \left(\frac{\arctan t}{\arctan t-t}\right)^2dt[/tex]

I honestly have no idea about how to proceed from here.

Any help is appreciated. Thanks!