What is the integral from 0 to 1 of 2^{5x} ?

The integral from 0 to 1 of 2^{5x} is (31)/(5ln(2))

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integral from 0 to 1 of 2^{5x}

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

\frac{31}{5 ln ( 2 )}

Decimal

8.94470 \dots

Solution steps

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

Simplify

2^{5 x} : 3 2^{x}

= \int_{0}^{1} 3 2^{x} d x

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

= [\frac{3 2 ^{x}}{ln ( 32 )}]_{0}^{1}

Simplify

ln (32) : 5 ln (2)

= [\frac{3 2 ^{x}}{5 ln ( 2 )}]_{0}^{1}

Compute the boundaries:

\frac{31}{5 ln ( 2 )}

= \frac{31}{5 ln ( 2 )}

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What is the integral from 0 to 1 of 2^{5x} ?
The integral from 0 to 1 of 2^{5x} is (31)/(5ln(2))