I like integrals 3

Calculus Level 4

π/2π/2ab2cosx(a2sin2x+b2cos2x)3/2dx \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 aa and bb.

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