I like integrals 3

Calculus Level 4

\[ \large \int_{-\pi/2}^{\pi /2} \dfrac{ab^2 \cos x}{ (a^2 \sin^2 x + b^2 \cos^2 x)^{3/2} } \, dx \]

Evaluate the integral above for positive constants \(a\) and \(b\).