Question

How do you integrate `int x^3 e^(4x) dx` using integration by parts?

Answer 1

Use integration by parts three times.

Explanation:

Each time choose a power of `x` as `u` and `dv = e^(4x) dx`

Each time you integrate, the power on `x` decreases and the coefficient of the next integral changes.

in the end you'll be able to facotr out a denominator and `e^(4x)` to finish with

`1/128e^(4x)(32x^3-24x^2+12x-3)+C`