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Step-by-step Solution

Integral of $\sqrt{e^{3x}}$

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Answer

$\frac{2}{3}e^{\frac{3}{2}x}+C_0$

Step-by-step explanation

Problem to solve:

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

Applying the power of a power property

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

Solve the integral $\int e^{\frac{3}{2}x}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=\frac{3}{2}x \\ du=1.5dx\end{matrix}$

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Answer

$\frac{2}{3}e^{\frac{3}{2}x}+C_0$
$\int\sqrt{e^{3x}}dx$

Main topic:

Integration by substitution

Used formulas:

1. See formulas

Time to solve it:

~ 0.76 seconds