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

The integral of (5^{ln(x)})/x is (5^{ln(x)})/(ln(5))+C

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integral of (5^{ln(x)})/x

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

\frac{5 ^{l n (x)}}{ln ( 5 )} + C

Solution steps

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

Apply u-substitution

= \int 5^{u} d u

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

= \frac{5 ^{u}}{ln ( 5 )}

Substitute back

u = ln (x)

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

Add a constant to the solution

= \frac{5 ^{l n (x)}}{ln ( 5 )} + C

What is the integral of (5^{ln(x)})/x ?
The integral of (5^{ln(x)})/x is (5^{ln(x)})/(ln(5))+C