Question

How do you integrate `x^4 e^x^5 dx`?

Answer 1

`int x^4e^(x^5) dx`

Use substitution to write this an an integral of `e^u du`

Let `u = x^5`. This makes `du = 5x^4 dx`,

`int x^4e^(x^5) dx = 1/5 int e^(x^5)(5x^4) dx = 1/5 int e^u du`

`=1/5 e^u +C = 1/5 e^(x^5) +C`

(Check by differentiating `1/5 e^(x^5) +C`)