How can I solve the integral below?

Question

How can I solve this? I've tried many ways, but it's all useless. Need help!

$$\int\frac{\mathrm dx}{a^2\sin^2x-b^2\cos^2x}$$

Answer 1

HINT:

Divide numerator & denominator by $\cos^2x$

Set $\tan x=u$

OR

Divide numerator & denominator by $\sin^2x$

Set $\cot x=v$