What is the integral of (ln(6x))/x ?

The integral of (ln(6x))/x is (ln^2(6x))/2+C

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integral of (ln(6x))/x

\int \frac{ln ( 6 x )}{x} d x

\frac{ln ^{2} ( 6 x )}{2} + C

Solution steps

\int \frac{ln ( 6 x )}{x} d x

Apply u-substitution

: \int \frac{ln ( u )}{u} d u

= \int \frac{ln ( u )}{u} d u

Apply u-substitution

: \int v d v

= \int v d v

Apply the Power Rule

: \frac{v ^{2}}{2}

= \frac{v ^{2}}{2}

Substitute back

= \frac{ln ^{2} ( 6 x )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( 6 x )}{2} + C

\int \frac{1}{( x ^{2} + a ^{2} ) ^{\frac{3}{2}}} d x

\int (cos (2 x) - sin (2 x))^{2} d x

\frac{d}{d x} ((4 x^{3} - 6) (4 x^{2} + 4))

\int \frac{1}{( 1 - x ^{2} ) ^{3}} d x

\frac{d}{d x} (\frac{ln ( x )}{9 x})

What is the integral of (ln(6x))/x ?
The integral of (ln(6x))/x is (ln^2(6x))/2+C