How do you integrate #e^(4x) dx#?

1 Answer
Jun 24, 2016

#1/4e^(4x)+C#

Explanation:

We will use the integration rule for #e^x#:

#inte^udu=e^u+C#

So, for the given integral, let #u=4x#. This implies that #du=4dx#.

#inte^(4x)dx=1/4inte^(4x)*4dx=1/4inte^udu=1/4e^u+C#

Since #u=4x#:

#1/4e^u+C=1/4e^(4x)+C#

We can differentiate this answer to check that we get #e^(4x)#. Indeed, through the chain rule, the #1/4# we had to add gets "undone" by the #4# coming from the power of #4x# via the chain rule.