What is the integral of (4^x)/(ln(4)) ?

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

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integral of (4^x)/(ln(4))

\int \frac{4 ^{x}}{ln ( 4 )} d x

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

Solution steps

\int \frac{4 ^{x}}{ln ( 4 )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{ln ( 4 )} \cdot \int 4^{x} d x

Simplify

ln (4) : 2 ln (2)

= \frac{1}{2 ln ( 2 )} \cdot \int 4^{x} d x

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

= \frac{1}{2 ln ( 2 )} \cdot \frac{4 ^{x}}{ln ( 4 )}

Simplify

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

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

Add a constant to the solution

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

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