What is the integral of ((ln(u))^4)/u ?

The integral of ((ln(u))^4)/u is (ln^5(u))/5+C

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integral of ((ln(u))^4)/u

\int \frac{( ln ( u ) ) ^{4}}{u} d u

\frac{ln ^{5} ( u )}{5} + C

Solution steps

\int \frac{( ln ( u ) ) ^{4}}{u} d u

Apply u-substitution

: \int v^{4} d v

= \int v^{4} d v

Apply the Power Rule

: \frac{v ^{5}}{5}

= \frac{v ^{5}}{5}

Substitute back

v = ln (u)

= \frac{ln ^{5} ( u )}{5}

Add a constant to the solution

= \frac{ln ^{5} ( u )}{5} + C

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What is the integral of ((ln(u))^4)/u ?
The integral of ((ln(u))^4)/u is (ln^5(u))/5+C