What is the antiderivative of #e^(2x) #?

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Answer 1 · 2016-02-13T21:35:01

#e^(2x)/2+C#

The antiderivative of #e^(2x)# is equivalent to

#=inte^(2x)dx#

Let #u=2x#, so #du=2dx#.

Here, we can make some substitutions:

#=inte^(2x)(1/2)2dx#

#=inte^u(1/2)du#

The #1/2# can be brought out of the integral:

#=1/2inte^udu#

Note that #inte^udu=e^u+C#, so

#=e^u/2+C#

#=e^(2x)/2+C#