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

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

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integral from 1 to 2 of (4^{ln(x)})/x

\int_{1}^{2} \frac{4 ^{l n (x)}}{x} d x

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

Decimal Notation

1.16430 \dots

Solution steps

\int_{1}^{2} \frac{4 ^{l n (x)}}{x} d x

Compute the indefinite integral:

\int \frac{4 ^{l n (x)}}{x} d x = \frac{2 ^{2 l n (x) - 1}}{ln ( 2 )} + C

Compute the boundaries:

\int_{1}^{2} \frac{4 ^{l n (x)}}{x} d x = \frac{2 ^{2 l n (2) - 1}}{ln ( 2 )} - \frac{1}{2 ln ( 2 )}

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

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