Evaluate: ∫ tan^3 x/(1+cos 2x) dx, x ∈[0, π/4]

Question

Evaluate:  

\(\int\limits_0^{\pi/4}\cfrac{tan^3x}{(1+cos\,2x)}dx\)

∫ tan³ x/(1+cos 2x) dx, x ∈[0, π/4]

Answer 1

Let \(I=\int\limits_0^{\pi/4}\cfrac{tan^3x}{(1+cos\,2x)}dx\)