Integrate $\int_0^{\pi/2}\frac{\cos^2x}{a\cos^2x + b\sin^2x}\,dx$ I don't know how to deal with this integral
$$I=\displaystyle\int_0^{\pi/2}\frac{\cos^2x}{a\cos^2x + b\sin^2x}\,dx$$
I reached the step
$$I
=\displaystyle\ \int_0^{\pi/2}\frac{1}{a + b\tan^2x}dx$$
Now what should I do? Please help.

put $\displaystyle I = \int^{\frac{\pi}{2}}\frac{\cos^2 x}{a\cos^2 x+b\sin^2 x}dx$ and $\displaystyle J = \int^{\frac{\pi}{2}}_{0}\frac{\sin^2 x}{a\cos^2 x+b\sin^2 x}dx$
$\displaystyle aI+bJ = \frac{\pi}{2}$ 
