Evaluate: ∫ sin x cos x/(cos^2x+3cosx+2)dx, x ∈[0, π/2]

Question

Evaluate:  

\(\int\limits_0^{\pi/2}\cfrac{sin\,x\,cos\,x}{(cos^2x+3cosx+2)}dx\)

∫ sin x cos x/(cos²x+3cosx+2)dx, x ∈[0, π/2]

Answer 1

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