Question

Evaluate: ∫ ((sin^–1 √x – cos^–1 √x)/ (sin^–1 √x + cos^–1 √x))  dx

Answer 1

= (4/π) ∫ sin^–1 √x dx –  ∫ dx 

Let x = sin² θ

= dx = sin 2θ dθ 

= (4/π) ∫ sin^–1 (sin θ) sin 2θ dθ – x + c 

= (4/π) ∫ θ sin 2θ dθ – x + c