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

The integral of e^{x/a} is ae^{x/a}+C

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integral of e^{x/a}

\int e^{\frac{x}{a}} d x

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

Solution steps

\int e^{\frac{x}{a}} d x

Apply u-substitution

= \int e^{u} a d u

Take the constant out:

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

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

Use the common integral:

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

= a e^{u}

Substitute back

u = \frac{x}{a}

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

Add a constant to the solution

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

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