What is the antiderivative of $e^{4 x}$ $e^(4x)$ ?

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Answer 1 · 2017-03-10T15:27:52

$\frac{1}{4} e^{4} x + C$ $1/4e^4x+C$

This will require a u-substitution.

$\int e^{4 x} d x$ $inte^(4x)dx$

Let $u = 4 x$ $u=4x$
$d u = 4 d x$ $du=4dx$
then
$\frac{1}{4} d u = d x$ $1/4du=dx$

The integral becomes:
$\frac{1}{4} \int e^{u} d u$ $1/4inte^udu$

Recall that the antiderivative of $e^{x}$ $e^x$ is equal to $e^{x}$ $e^x$

So, $\frac{1}{4} \int e^{u} d u = \frac{1}{4} e^{u} = \frac{1}{4} e^{4 x} + C$ $1/4inte^udu=1/4e^u=1/4e^(4x)+C$

Never forget the constant of integration.

What is the antiderivative of e4xe^(4x)?