What is the antiderivative of #e^(4x)#?

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Answer 1 · 2017-03-10T15:27:52

#1/4e^4x+C#

This will require a u-substitution.

#inte^(4x)dx#

Let #u=4x#
#du=4dx#
then
#1/4du=dx#

The integral becomes:
#1/4inte^udu#

Recall that the antiderivative of #e^x# is equal to #e^x#

So, #1/4inte^udu=1/4e^u=1/4e^(4x)+C#

Never forget the constant of integration.