What is the integral of ((ln(u))^5)/u ?

The integral of ((ln(u))^5)/u is (ln^6(u))/6+C

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integral of ((ln(u))^5)/u

\int \frac{( ln ( u ) ) ^{5}}{u} d u

\frac{ln ^{6} ( u )}{6} + C

Solution steps

\int \frac{( ln ( u ) ) ^{5}}{u} d u

Apply u-substitution

: \int v^{5} d v

= \int v^{5} d v

Apply the Power Rule

: \frac{v ^{6}}{6}

= \frac{v ^{6}}{6}

Substitute back

v = ln (u)

= \frac{ln ^{6} ( u )}{6}

Add a constant to the solution

= \frac{ln ^{6} ( u )}{6} + C

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What is the integral of ((ln(u))^5)/u ?
The integral of ((ln(u))^5)/u is (ln^6(u))/6+C