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

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

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

\int \frac{4 ^{l n (x)}}{x} d x

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

Solution steps

\int \frac{4 ^{l n (x)}}{x} d x

Apply u-substitution

: \int 4^{u} d u

= \int 4^{u} d u

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

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

Substitute back

u = ln (x)

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

Simplify

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

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

Add a constant to the solution

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

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