Question

integrate (lnt)^2dt

Answer 1

\[ \int \left[ \ln(t) \right]^2 dt \]
?

Answer 2

yes

Answer 3

Integrate by parts:
\[ \int \ln^2(t) dt = t\cdot \ln^2(t) - \int 2\cdot t \cdot \ln(t) \cdot \frac{1}{t} dt\]
\[= t\cdot \ln^2(t) - 2\int \ln(t) dt = t\cdot \ln^2(t) - 2\left[t \cdot \ln(t) - \int dt \right]\]
\[ = t\cdot \ln^2(t) - 2t \cdot \ln(t) +2t + C\]

Answer 4

Thanks!!

Answer 5

Sure