What is the integral from 0 to 1 of a^x ?

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

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integral from 0 to 1 of a^x

\int_{0}^{1} a^{x} d x

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

Solution steps

\int_{0}^{1} a^{x} d x

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

= [\frac{a ^{x}}{ln ( a )}]_{0}^{1}

Compute the boundaries:

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

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

Simplify

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

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