What is the integral from 0 to log_{5 of (2)}5^x ?

The integral from 0 to log_{5 of (2)}5^x is 1/(ln(5))

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integral from 0 to log_{5 of (2)}5^x

\int_{0}^{l o g_{5} (2)} 5^{x} d x

\frac{1}{ln ( 5 )}

Decimal Notation

0.62133 \dots

Solution steps

\int_{0}^{l o g_{5} (2)} 5^{x} d x

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

= [\frac{5 ^{x}}{ln ( 5 )}]_{0}^{l o g_{5} (2)}

Compute the boundaries:

\frac{1}{ln ( 5 )}

= \frac{1}{ln ( 5 )}

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What is the integral from 0 to log_{5 of (2)}5^x ?
The integral from 0 to log_{5 of (2)}5^x is 1/(ln(5))