Question

How would you go about integrating x^2/sqrt(4-x^2)?

Answer 1

let

x = 2sinθ
4-x^2 = 4-4sin^2θ = 4cos^2θ
dx = 2cosθ dθ

Then you have

∫ x^2/√(4-x^2) dx
= ∫4sin^2θ/2cosθ * 2cosθ dθ
= ∫4sin^2θ dθ
= ∫2(1-cos2θ) dθ
...