Evaluate the integral by using a substitution prior to integration by parts.
-$$\int ( \ln 3 x ) ^ { 2 } d x$$
A) $x ( \ln 3 x ) ^ { 2 } - 2 x ( \ln 3 x ) + 2 x + C$
B) $x ( \ln 3 x ) ^ { 2 } + 2 x ( \ln 3 x ) - 2 x + C$
C) $x ( \ln 3 x ) ^ { 2 } - x ( \ln 3 x ) + x + C$
D) $x ( \ln 3 x ) ^ { 2 } - 2 x ( \ln 3 x ) + C$

Question

Quizplus · Accepted Answer

First, let $u = \ln(3x)$, then $du = \frac{1}{x}dx$, and $x dx = x du$. Using integration by parts with $u$ and $dv = x du$, we find the integral to be $x(\ln 3x)^2 - 2x(\ln 3x) + 2x + C$.

Evaluate the Integral by Using a Substitution Prior to Integration ∫(ln⁡3x)2dx\int ( \ln 3 x ) ^ { 2 } d x∫(ln3x)2dx

Evaluate the Integral by Using a Substitution Prior to Integration $\int ( \ln 3 x ) ^ { 2 } d x$