What is the integral of ((ln(t))^2)/t ?

The integral of ((ln(t))^2)/t is (ln^3(t))/3+C

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integral of ((ln(t))^2)/t

\int \frac{( ln ( t ) ) ^{2}}{t} d t

\frac{ln ^{3} ( t )}{3} + C

Solution steps

\int \frac{( ln ( t ) ) ^{2}}{t} d t

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = ln (t)

= \frac{ln ^{3} ( t )}{3}

Add a constant to the solution

= \frac{ln ^{3} ( t )}{3} + C

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What is the integral of ((ln(t))^2)/t ?
The integral of ((ln(t))^2)/t is (ln^3(t))/3+C