Find the Integral 2e^(2x)

$2 e^{2 x}$

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int e^{2 x} d x$

Let $u = 2 x$ . Then $d u = 2 d x$ , so $\frac{1}{2} d u = d x$ . Rewrite using $u$ and $d$ $u$ .

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Let $u = 2 x$ . Find $\frac{d u}{d x}$ .

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Rewrite.

$\frac{2}{1}$

Divide $2$ by $1$ .

$2$

Rewrite the problem using $u$ and $d u$ .

$2 \int e^{u} \frac{1}{2} d u$

Combine $e^{u}$ and $\frac{1}{2}$ .

$2 \int \frac{e^{u}}{2} d u$

Since $\frac{1}{2}$ is constant with respect to $u$ , move $\frac{1}{2}$ out of the integral.

$2 (\frac{1}{2} \int e^{u} d u)$

Simplify.

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Combine $\frac{1}{2}$ and $2$ .

$\frac{2}{2} \int e^{u} d u$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2}{2} \int e^{u} d u$

Divide $1$ by $1$ .

$1 \int e^{u} d u$

Multiply $\int e^{u} d u$ by $1$ .

$\int e^{u} d u$

The integral of $e^{u}$ with respect to $u$ is $e^{u}$ .

$e^{u} + C$

Replace all occurrences of $u$ with $2 x$ .

$e^{2 x} + C$

Find the Integral 2e^(2x)

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