What is the integral from 1 to 3 of 4^{5x} ?

The integral from 1 to 3 of 4^{5x} is (107374080)/(ln(2))

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integral from 1 to 3 of 4^{5x}

\int_{1}^{3} 4^{5 x} d x

\frac{107374080}{ln ( 2 )}

Decimal

154908052.73601 \dots

Solution steps

\int_{1}^{3} 4^{5 x} d x

Simplify

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

= \int_{1}^{3} 102 4^{x} d x

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

= [\frac{102 4 ^{x}}{ln ( 1024 )}]_{1}^{3}

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

= [\frac{2 ^{10 x - 1}}{5 ln ( 2 )}]_{1}^{3}

Compute the boundaries:

\frac{107374080}{ln ( 2 )}

= \frac{107374080}{ln ( 2 )}

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\int_{1}^{2} \frac{1}{x ^{5} + x ^{3}} d x

\int_{\frac{π}{3}}^{x} sec^{2} (t) d t

What is the integral from 1 to 3 of 4^{5x} ?
The integral from 1 to 3 of 4^{5x} is (107374080)/(ln(2))