Question

What is the antiderivative of `e^(4x)`?

Answer 1

`1/4e^4x+C`

Explanation:

This will require a u-substitution.

`inte^(4x)dx`

Let `u=4x`
`du=4dx`
then
`1/4du=dx`

The integral becomes:
`1/4inte^udu`

Recall that the antiderivative of `e^x` is equal to `e^x`

So, `1/4inte^udu=1/4e^u=1/4e^(4x)+C`

Never forget the constant of integration.