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

The integral of e^{x/pi} is pie^{x/pi}+C

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integral of e^{x/pi}

\int e^{\frac{x}{π}} d x

π e^{\frac{x}{π}} + C

Solution steps

\int e^{\frac{x}{π}} d x

Apply u-substitution

= \int e^{u} π d u

Take the constant out:

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

= π \cdot \int e^{u} d u

Use the common integral:

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

= π e^{u}

Substitute back

u = \frac{x}{π}

= π e^{\frac{x}{π}}

Add a constant to the solution

= π e^{\frac{x}{π}} + C