What is the integral from 0 to 3 of 2^{4x} ?

The integral from 0 to 3 of 2^{4x} is (4095)/(4ln(2))

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integral from 0 to 3 of 2^{4x}

\int_{0}^{3} 2^{4 x} d x

\frac{4095}{4 ln ( 2 )}

Decimal

1476.95904 \dots

Solution steps

\int_{0}^{3} 2^{4 x} d x

Simplify

2^{4 x} : 1 6^{x}

= \int_{0}^{3} 1 6^{x} d x

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

= [\frac{1 6 ^{x}}{ln ( 16 )}]_{0}^{3}

\frac{1 6 ^{x}}{ln ( 16 )} = \frac{2 ^{4 x - 2}}{ln ( 2 )}

= [\frac{2 ^{4 x - 2}}{ln ( 2 )}]_{0}^{3}

Compute the boundaries:

\frac{4095}{4 ln ( 2 )}

= \frac{4095}{4 ln ( 2 )}

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What is the integral from 0 to 3 of 2^{4x} ?
The integral from 0 to 3 of 2^{4x} is (4095)/(4ln(2))