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

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

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integral of (ln(v))/v

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

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

Solution steps

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

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 (v)

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

Add a constant to the solution

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

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