What is the integral from 0 to e of a^x ?

The integral from 0 to e of a^x is (a^e-1)/(ln(a))

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integral from 0 to e of a^x

\int_{0}^{e} a^{x} d x

\frac{a ^{e} - 1}{ln ( a )}

Solution steps

\int_{0}^{e} a^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= [\frac{a ^{x}}{ln ( a )}]_{0}^{e}

Compute the boundaries:

\frac{a ^{e}}{ln ( a )} - \frac{1}{ln ( a )}

= \frac{a ^{e}}{ln ( a )} - \frac{1}{ln ( a )}

Simplify

= \frac{a ^{e} - 1}{ln ( a )}

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What is the integral from 0 to e of a^x ?
The integral from 0 to e of a^x is (a^e-1)/(ln(a))