What is the integral of \sqrt[10]{e^x} ?

The integral of \sqrt[10]{e^x} is 10e^{x/(10)}+C

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integral of \sqrt[10]{e^x}

10 e^{\frac{x}{10}} + C

Solution steps

Apply radical rule:

assuming

a \geq 0

= \int e^{\frac{x}{10}} d x

Apply u-substitution

: \int e^{u} \cdot 10 d u

= \int e^{u} \cdot 10 d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= 10 e^{u}

Substitute back

u = \frac{x}{10}

= 10 e^{\frac{x}{10}}

Add a constant to the solution

= 10 e^{\frac{x}{10}} + C

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What is the integral of \sqrt[10]{e^x} ?
The integral of \sqrt[10]{e^x} is 10e^{x/(10)}+C