What is the integral from 0 to 1 of 15^{2x} ?

The integral from 0 to 1 of 15^{2x} is (112)/(ln(15))

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integral from 0 to 1 of 15^{2x}

\int_{0}^{1} 1 5^{2 x} d x

\frac{112}{ln ( 15 )}

Decimal

41.35816 \dots

Solution steps

\int_{0}^{1} 1 5^{2 x} d x

Simplify

1 5^{2 x} : 22 5^{x}

= \int_{0}^{1} 22 5^{x} d x

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

= [\frac{22 5 ^{x}}{ln ( 225 )}]_{0}^{1}

Simplify

ln (225) : 2 ln (15)

= [\frac{22 5 ^{x}}{2 ln ( 15 )}]_{0}^{1}

Compute the boundaries:

\frac{112}{ln ( 15 )}

= \frac{112}{ln ( 15 )}

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What is the integral from 0 to 1 of 15^{2x} ?
The integral from 0 to 1 of 15^{2x} is (112)/(ln(15))