Question

How do you find the integral of `int (x^2)(e)^(-x^3) dx` from negative infinity to infinity?

Answer 1

`+oo`

Explanation:

`-x^3=t => -3x^2dx=dt => x^2dx=-dt/3`

`int x^2e^(-x^3)dx=-1/3inte^tdt=-1/3e^(-x^3)+C`

`I=int_-oo^(+oo) x^2e^(-x^3)dx= -1/3e^(-x^3)|_-oo^(+oo)`

`I=-1/3lim_(x->+oo) e^(-x^3) + 1/3lim_(x->-oo) e^(-x^3)`

`I=0+oo=+oo`