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

1 Answer
Oct 16, 2016

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#