What is the integral of (ln(20x))/x ?

The integral of (ln(20x))/x is (ln^2(20x))/2+C

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integral of (ln(20x))/x

\int \frac{ln ( 20 x )}{x} d x

\frac{ln ^{2} ( 20 x )}{2} + C

Solution steps

\int \frac{ln ( 20 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} ( 20 x )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( 20 x )}{2} + C

\frac{d}{d y} (- e^{y})

\frac{d ^{2} y}{d x ^{2}} + 16 y = 0

f (x) = - x^{3} + 2 x - e^{- x} - 3

\frac{3}{\frac{s + 2}{s}}

\frac{\partial}{\partial x} (2 x^{4} + 5 y^{2} + x y)

What is the integral of (ln(20x))/x ?
The integral of (ln(20x))/x is (ln^2(20x))/2+C