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

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Answer 1 · 2016-10-16T18:50:42

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

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

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