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

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

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

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

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

Solution steps

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

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 (n)

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

Add a constant to the solution

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

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