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

The integral of e^{x/l} is le^{x/l}+C

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integral of e^{x/l}

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

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

Solution steps

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

Apply u-substitution

= \int e^{u} l d u

Take the constant out:

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

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

Use the common integral:

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

= l e^{u}

Substitute back

u = \frac{x}{l}

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

Add a constant to the solution

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

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