What is the integral from 0 to log_{9 of (2)}9^x ?

The integral from 0 to log_{9 of (2)}9^x is 1/(2ln(3))

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integral from 0 to log_{9 of (2)}9^x

\int_{0}^{l o g_{9} (2)} 9^{x} d x

\frac{1}{2 ln ( 3 )}

Decimal

0.45511 \dots

Solution steps

\int_{0}^{l o g_{9} (2)} 9^{x} d x

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

= [\frac{9 ^{x}}{ln ( 9 )}]_{0}^{l o g_{9} (2)}

Simplify

ln (9) : 2 ln (3)

= [\frac{9 ^{x}}{2 ln ( 3 )}]_{0}^{l o g_{9} (2)}

Compute the boundaries:

\frac{1}{2 ln ( 3 )}

= \frac{1}{2 ln ( 3 )}

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What is the integral from 0 to log_{9 of (2)}9^x ?
The integral from 0 to log_{9 of (2)}9^x is 1/(2ln(3))