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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int \frac{3 ^{l n (u)}}{u} d u

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

Apply u-substitution

: \int 3^{v} d v

= \int 3^{v} d v

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

= \frac{3 ^{v}}{ln ( 3 )}

Substitute back

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

Add a constant to the solution

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

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