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

Oct 16, 2016

Use integration by parts three times.

#### Explanation:

Each time choose a power of $x$ as $u$ and $\mathrm{dv} = {e}^{4 x} \mathrm{dx}$

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 ${e}^{4 x}$ to finish with

$\frac{1}{128} {e}^{4 x} \left(32 {x}^{3} - 24 {x}^{2} + 12 x - 3\right) + C$