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

The integral of (ln(3x))/x is (ln^2(3x))/2+C

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integral of (ln(3x))/x

\int \frac{ln ( 3 x )}{x} d x

\frac{ln ^{2} ( 3 x )}{2} + C

Solution steps

\int \frac{ln ( 3 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} ( 3 x )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( 3 x )}{2} + C

x^{2} + 3 x - 4

x^{2} - 3 x

x \to - \infty lim (2 x^{3})

x \to 0 lim ((1 + 8 x)^{\frac{7}{x}})

(2, - 3), (7, 12)

What is the integral of (ln(3x))/x ?
The integral of (ln(3x))/x is (ln^2(3x))/2+C