What is the integral of 1/(sqrt(e^{2x))} ?

The integral of 1/(sqrt(e^{2x))} is -1/(e^x)+C

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integral of 1/(sqrt(e^{2x))}

\int \frac{1}{e ^{2 x}} d x

- \frac{1}{e ^{x}} + C

Solution steps

\int \frac{1}{e ^{2 x}} d x

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = e^{2 x}

= - \frac{1}{e ^{2 x}}

Simplify

- \frac{1}{e ^{2 x}} : - \frac{1}{e ^{x}}

= - \frac{1}{e ^{x}}

Add a constant to the solution

= - \frac{1}{e ^{x}} + C

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What is the integral of 1/(sqrt(e^{2x))} ?
The integral of 1/(sqrt(e^{2x))} is -1/(e^x)+C