What is the integral of (ln(9x))/x ?

The integral of (ln(9x))/x is (ln^2(9x))/2+C

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integral of (ln(9x))/x

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

\frac{ln ^{2} ( 9 x )}{2} + C

Solution steps

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

Apply u-substitution

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

Apply u-substitution

= \int v d v

Apply the Power Rule

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

Substitute back

= \frac{ln ^{2} ( 9 x )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( 9 x )}{2} + C

\int (1 - x) (1 - 2 x) (1 - 3 x) d x

\int \frac{x ^{8}}{x ^{9} - 2} d x

\int_{0}^{5} x e^{- x} d x

\int cos (8)

\frac{d y}{d x} + \frac{( y ^{2} )}{x ^{2}} = 0

What is the integral of (ln(9x))/x ?
The integral of (ln(9x))/x is (ln^2(9x))/2+C