# Step-by-step Solution

## Integral of $\frac{1}{3}e^{3x}$

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### Videos

$\frac{1}{9}e^{3x}+C_0$

## Step-by-step explanation

Problem to solve:

$\int\frac{1}{3} e^{3x}dx$
1

Take the constant out of the integral

$\frac{1}{3}\int e^{3x}dx$
2

Solve the integral $\int e^{3x}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=3x \\ du=3dx\end{matrix}$

$\frac{1}{9}e^{3x}+C_0$
$\int\frac{1}{3} e^{3x}dx$

### Main topic:

Integration by substitution

~ 1.37 seconds

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