What is the integral of e^{1/5 x} ?

The integral of e^{1/5 x} is 5e^{1/5 x}+C

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integral of e^{1/5 x}

\int e^{\frac{1}{5} x} d x

5 e^{\frac{1}{5} x} + C

Solution steps

\int e^{\frac{1}{5} x} d x

Apply u-substitution

: \int e^{u} \cdot 5 d u

= \int e^{u} \cdot 5 d u

Take the constant out:

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

= 5 \cdot \int e^{u} d u

Use the common integral:

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

= 5 e^{u}

Substitute back

u = \frac{1}{5} x

= 5 e^{\frac{1}{5} x}

Add a constant to the solution

= 5 e^{\frac{1}{5} x} + C

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