Question

Evaluate `int (x sin^-1 (x^2))/sqrt(1 - x^4) dx`.

Answer 1

Given that `int (x sin^-1 (x^2))/sqrt(1 - x^4) dx`

Put sin^–1(x²) = y

⇒ `x/sqrt(1 - x^4) dx = dy/2`

⇒ `1/2 int y  dy = 1/4 xx y^2 + C`

∴ `int (x sin^-1(x^2))/sqrt(1 - x^4) dx = 1/4 (sin^-1(x^2))^2 + C`