What is the integral of (ln(7x))/x ?

The integral of (ln(7x))/x is (ln^2(7x))/2+C

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integral of (ln(7x))/x

\int \frac{ln ( 7 x )}{x} d x

\frac{ln ^{2} ( 7 x )}{2} + C

Solution steps

\int \frac{ln ( 7 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} ( 7 x )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( 7 x )}{2} + C

y = cos (x)

\frac{d}{d t} (- 3 t)

f (x) = \frac{x}{5}

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

\frac{d}{d x} (x^{3} - 3 x^{2} - 9 x + 1)

What is the integral of (ln(7x))/x ?
The integral of (ln(7x))/x is (ln^2(7x))/2+C