Question

`intx^2/sqrt(1 - x^6)dx` is equal to ______ 

Options

• `sin^-1 x^2 + c`

• `2/3 sin^-1x^3 + c`

• `1/3sin^-1 x^3 + c`

• `1/2sin^-1x^2 + c`

Answer 1

`intx^2/sqrt(1 - x^6)dx` is equal to `underline(1/3sin^-1 x^3 + c)`.

Explanation:

Let I = `intx^2/sqrt(1 - x^6)dx`

= `intx^2/sqrt(1 - (x^3)^2)dx`

Put x³ = t ⇒ 3x² dx = dt

∴ I = `1/3int1/sqrt(1 - t^2)dt`

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

∴ I = `1/3sin^-1(x^3) + c`