What is the integral from 1 to 4 of 4^{5x} ?

The integral from 1 to 4 of 4^{5x} is (2^{39}-512)/(5ln(2))

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integral from 1 to 4 of 4^{5x}

\int_{1}^{4} 4^{5 x} d x

\frac{2 ^{39} - 512}{5 ln ( 2 )}

Decimal

158625997131.48672

Solution steps

\int_{1}^{4} 4^{5 x} d x

Simplify

4^{5 x} : 102 4^{x}

= \int_{1}^{4} 102 4^{x} d x

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

= [\frac{102 4 ^{x}}{ln ( 1024 )}]_{1}^{4}

\frac{102 4 ^{x}}{ln ( 1024 )} = \frac{2 ^{10 x - 1}}{5 ln ( 2 )}

= [\frac{2 ^{10 x - 1}}{5 ln ( 2 )}]_{1}^{4}

Compute the boundaries:

\frac{2 ^{39} - 512}{5 ln ( 2 )}

= \frac{2 ^{39} - 512}{5 ln ( 2 )}

What is the integral from 1 to 4 of 4^{5x} ?
The integral from 1 to 4 of 4^{5x} is (2^{39}-512)/(5ln(2))