I'm trying to solve this integral - $\int_0^{\pi/2}{dx\over{4+9\cos^2x}}$
I've started by dividing numerator and denominator by $\cos^2x$
$\int_0^{\pi/2}{{dx\over{\cos^2x}}\over{{4+9\cos^2x}\over{\cos^2x}}}$
which gives me
$\int_0^{\pi/2}{{\sec^2x}{dx}\over{4{\sec^2x}+9}}$
I cant go any further. Can someone help / point me in the right direction please?