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

The integral of (3^{ln(x^5)})/x is (243^{ln(x)})/(5ln(3))+C

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

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

\frac{24 3 ^{l n (x)}}{5 ln ( 3 )} + C

Solution steps

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

Simplify

\frac{3 ^{l n (x^{5})}}{x} : \frac{24 3 ^{l n (x)}}{x}

= \int \frac{24 3 ^{l n (x)}}{x} d x

Apply u-substitution

: \int 24 3^{u} d u

= \int 24 3^{u} d u

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

= \frac{24 3 ^{u}}{ln ( 243 )}

Substitute back

u = ln (x)

= \frac{24 3 ^{l n (x)}}{ln ( 243 )}

Simplify

ln (243) : 5 ln (3)

= \frac{24 3 ^{l n (x)}}{5 ln ( 3 )}

Add a constant to the solution

= \frac{24 3 ^{l n (x)}}{5 ln ( 3 )} + C

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What is the integral of (3^{ln(x^5)})/x ?
The integral of (3^{ln(x^5)})/x is (243^{ln(x)})/(5ln(3))+C