Question

What is the antiderivative of (Ln 3x)^2

Answer 1

\[\int\limits \left( \ln 3x \right)^2*1dx=\left( \ln 3x \right)^2*x-\int\limits \frac{ 2\ln 3x*3 }{ 3x }*x~dx\]

Answer 2

\[=\left( \ln 3x \right)^2*x-2\left[ \left( \ln 3x \right)*x-\int\limits \frac{ 3 }{ 3x }*x~dx \right]+c\]
\[=\left( \ln 3x \right)^2*x-2x*\ln 3x+2x+c\]
i have used integrate by parts.