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

$=e^u/2+C$

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

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