Need help with a definite integral $\int_0^{\infty} \frac{x-1}{\sqrt{2^x-1}\ln(2^x-1)}\,dx$ [duplicate]
Try $t=\tan\theta$
Simplify everything in terms of $\sin$ and $\cos$. Substitute $\pi/2-\theta=\phi$ and add and do what you do with other definite questions. Be sure to completely simplify your numerator to break into two integrals.