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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{u ^{6}}{6}

Substitute back

u = ln (t)

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

Add a constant to the solution

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

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