What is the integral from 1 to 5 of (5^{ln(x)})/x ?

The integral from 1 to 5 of (5^{ln(x)})/x is (5^{ln(5)}-1)/(ln(5))

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integral from 1 to 5 of (5^{ln(x)})/x

\int_{1}^{5} \frac{5 ^{l n (x)}}{x} d x

\frac{5 ^{l n (5)} - 1}{ln ( 5 )}

Decimal Notation

7.66332 \dots

Solution steps

\int_{1}^{5} \frac{5 ^{l n (x)}}{x} d x

Apply u-substitution

: \int_{0}^{l n (5)} 5^{u} d u

= \int_{0}^{l n (5)} 5^{u} d u

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

= [\frac{5 ^{u}}{ln ( 5 )}]_{0}^{l n (5)}

Compute the boundaries:

\frac{5 ^{l n (5)} - 1}{ln ( 5 )}

= \frac{5 ^{l n (5)} - 1}{ln ( 5 )}

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What is the integral from 1 to 5 of (5^{ln(x)})/x ?
The integral from 1 to 5 of (5^{ln(x)})/x is (5^{ln(5)}-1)/(ln(5))