What is the integral of (ln(r))/r ?

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

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integral of (ln(r))/r

\int \frac{ln ( r )}{r} d r

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

Solution steps

\int \frac{ln ( r )}{r} d r

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 (r)

= \frac{ln ^{2} ( r )}{2}

Add a constant to the solution

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

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