What is the integral from 0 to 1 of 3^{4x} ?

The integral from 0 to 1 of 3^{4x} is (20)/(ln(3))

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integral from 0 to 1 of 3^{4x}

\int_{0}^{1} 3^{4 x} d x

\frac{20}{ln ( 3 )}

Decimal

18.20478 \dots

Solution steps

\int_{0}^{1} 3^{4 x} d x

Simplify

3^{4 x} : 8 1^{x}

= \int_{0}^{1} 8 1^{x} d x

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

= [\frac{8 1 ^{x}}{ln ( 81 )}]_{0}^{1}

Simplify

ln (81) : 4 ln (3)

= [\frac{8 1 ^{x}}{4 ln ( 3 )}]_{0}^{1}

Compute the boundaries:

\frac{20}{ln ( 3 )}

= \frac{20}{ln ( 3 )}

What is the integral from 0 to 1 of 3^{4x} ?
The integral from 0 to 1 of 3^{4x} is (20)/(ln(3))