What is the integral of (ln(x))/(sqrt(x^2)) ?

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

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integral of (ln(x))/(sqrt(x^2))

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

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

Solution steps

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

x^{2} = (x),

assuming

x \geq 0

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

Add a constant to the solution

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

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