Question

`int x^2/sqrt(1 - x^6)dx` = ______.

Options

• `-sin^-1 (x^3) + c`

• `cos^-1 (x^3) + c`

• `sin^-1 (x^3) + c`

• `1/3 sin^-1 (x^3) + c`

Answer 1

`int x^2/sqrt(1 - x^6)dx` = `underlinebb(1/3 sin^-1 (x^3) + c)`.

Explanation:

`int x^2/sqrt(1 - x^6)dx`

∴ Put x³ = t

`\implies` 3x²dx = dt

`\implies` x²dx = `dt/3`

∴ I = `1/3 int dt/sqrt(1 - t^2)`

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

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