What is the integral of (5^{3ln(x)})/x ?

The integral of (5^{3ln(x)})/x is (125^{ln(x)})/(3ln(5))+C

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integral of (5^{3ln(x)})/x

\int \frac{5 ^{3 l n (x)}}{x} d x

\frac{12 5 ^{l n (x)}}{3 ln ( 5 )} + C

Solution steps

\int \frac{5 ^{3 l n (x)}}{x} d x

5^{3 l n (x)} = 12 5^{l n (x)}

= \int \frac{12 5 ^{l n (x)}}{x} d x

Apply u-substitution

: \int 12 5^{u} d u

= \int 12 5^{u} d u

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

= \frac{12 5 ^{u}}{ln ( 125 )}

Substitute back

u = ln (x)

= \frac{12 5 ^{l n (x)}}{ln ( 125 )}

Simplify

ln (125) : 3 ln (5)

= \frac{12 5 ^{l n (x)}}{3 ln ( 5 )}

Add a constant to the solution

= \frac{12 5 ^{l n (x)}}{3 ln ( 5 )} + C

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What is the integral of (5^{3ln(x)})/x ?
The integral of (5^{3ln(x)})/x is (125^{ln(x)})/(3ln(5))+C