What is the integral of (ln^3(z))/z ?

The integral of (ln^3(z))/z is (ln^4(z))/4+C

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integral of (ln^3(z))/z

\int \frac{ln ^{3} ( z )}{z} d z

\frac{ln ^{4} ( z )}{4} + C

Solution steps

\int \frac{ln ^{3} ( z )}{z} d z

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = ln (z)

= \frac{ln ^{4} ( z )}{4}

Add a constant to the solution

= \frac{ln ^{4} ( z )}{4} + C

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What is the integral of (ln^3(z))/z ?
The integral of (ln^3(z))/z is (ln^4(z))/4+C