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

The integral of (ln(t))^2 is tln^2(t)-2(tln(t)-t)+C

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integral of (ln(t))^2

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

t ln^{2} (t) - 2 (t ln (t) - t) + C

Solution steps

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

Apply Integration By Parts

: t ln^{2} (t) - \int 2 ln (t) d t

= t ln^{2} (t) - \int 2 ln (t) d t

\int 2 ln (t) d t = 2 (t ln (t) - t)

= t ln^{2} (t) - 2 (t ln (t) - t)

Add a constant to the solution

= t ln^{2} (t) - 2 (t ln (t) - t) + C

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What is the integral of (ln(t))^2 ?
The integral of (ln(t))^2 is tln^2(t)-2(tln(t)-t)+C