Question

`f x^2 e^(x^3) dx` equals

Options

• `1/3 e^(x^3) + c`

• `1/3 e^(x^2) + c`

• `1/2 e^(x^3) + c`

• `1/2 e^(x^2) + c`

Answer 1

`1/3 e^(x^3) + c`

Explanation:

`f x^2 e^(x^3) dx` put `x^3 = t`

∴ `3x^2 dx = dt`

= `1/3 int (3x^2)e^(x^3) dx`

= `1/3 int e^t dt`

= `1/3 e^t + c`

= `1/3 e^(x^3) + c`