What is the integral from 0 to 1 of 3^{5x} ?

The integral from 0 to 1 of 3^{5x} is (242)/(5ln(3))

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integral from 0 to 1 of 3^{5x}

\int_{0}^{1} 3^{5 x} d x

\frac{242}{5 ln ( 3 )}

Decimal

44.05557 \dots

Solution steps

\int_{0}^{1} 3^{5 x} d x

Simplify

3^{5 x} : 24 3^{x}

= \int_{0}^{1} 24 3^{x} d x

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

= [\frac{24 3 ^{x}}{ln ( 243 )}]_{0}^{1}

Simplify

ln (243) : 5 ln (3)

= [\frac{24 3 ^{x}}{5 ln ( 3 )}]_{0}^{1}

Compute the boundaries:

\frac{242}{5 ln ( 3 )}

= \frac{242}{5 ln ( 3 )}

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What is the integral from 0 to 1 of 3^{5x} ?
The integral from 0 to 1 of 3^{5x} is (242)/(5ln(3))