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

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

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integral of (ln|x|)/x

\int \frac{ln ∣ x ∣}{x} d x

\frac{ln ∣ x ∣ ^{2}}{2} + C

Solution steps

\int \frac{ln ∣ x ∣}{x} d x

\frac{ln ∣ x ∣}{x} = ln ∣ x ∣ \frac{1}{x}

= \int ln ∣ x ∣ \frac{1}{x} d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = ln ∣ x ∣

= \frac{ln ∣ x ∣ ^{2}}{2}

Add a constant to the solution

= \frac{ln ∣ x ∣ ^{2}}{2} + C

f (t) = (3 t - 1)^{4} (2 t + 1)^{- 3}

x \to 0 lim (\frac{tan ( k x )}{x})

\int z^{3} e^{z} d z

\frac{d}{d x} (arctan (ln (x^{2})))

\frac{d}{d x} (ln (2 x))