What is the integral of ((ln(u))^6)/u ?

The integral of ((ln(u))^6)/u is (ln^7(u))/7+C

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integral of ((ln(u))^6)/u

\int \frac{( ln ( u ) ) ^{6}}{u} d u

\frac{ln ^{7} ( u )}{7} + C

Solution steps

\int \frac{( ln ( u ) ) ^{6}}{u} d u

Apply u-substitution

: \int v^{6} d v

= \int v^{6} d v

Apply the Power Rule

: \frac{v ^{7}}{7}

= \frac{v ^{7}}{7}

Substitute back

v = ln (u)

= \frac{ln ^{7} ( u )}{7}

Add a constant to the solution

= \frac{ln ^{7} ( u )}{7} + C

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What is the integral of ((ln(u))^6)/u ?
The integral of ((ln(u))^6)/u is (ln^7(u))/7+C