# Math virtual assistant

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# Step-by-step Solution

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## Answer

$5\left(\frac{1}{2}e^{2x}x-\frac{1}{4}e^{2x}\right)+C_0$

## Step-by-step explanation

Problem to solve:

$\int5x e^{2x}dx$
1

Take the constant out of the integral

$5\int xe^{2x}dx$
2

Use the integration by parts theorem to calculate the integral $\int xe^{2x}dx$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

## Answer

$5\left(\frac{1}{2}e^{2x}x-\frac{1}{4}e^{2x}\right)+C_0$
$\int5x e^{2x}dx$

### Main topic:

Integration by substitution

~ 0.71 seconds

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