Question

Integrate the following w.r.t.x : `x^2/sqrt(1 - x^6)`

Answer 1

Let I = `int x^2/sqrt(1 - x^6)*dx`
Put x³ = t
∴ 3x²dx = dt

∴ x²dx = `(1)/(3)*dt`

∴ I = `(1)/(3) int 1/sqrt(1 - t^2)*dt`

= `(1)/(3)sin^-1 (t) + c`

= `(1)/(3)sin^-1 (x^3) + c`.