What is the integral of sqrt(2^{4x)} ?

The integral of sqrt(2^{4x)} is (2^{2x-1})/(ln(2))+C

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integral of sqrt(2^{4x)}

\int 2^{4 x} d x

\frac{2 ^{2 x - 1}}{ln ( 2 )} + C

Solution steps

\int 2^{4 x} d x

Simplify

2^{4 x} : 4^{x}

= \int 4^{x} d x

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

= \frac{4 ^{x}}{ln ( 4 )}

Simplify

\frac{4 ^{x}}{ln ( 4 )} : \frac{2 ^{2 x - 1}}{ln ( 2 )}

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

Add a constant to the solution

= \frac{2 ^{2 x - 1}}{ln ( 2 )} + C

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What is the integral of sqrt(2^{4x)} ?
The integral of sqrt(2^{4x)} is (2^{2x-1})/(ln(2))+C