Use a table of integrals to find the indefinite integral $\int ( \ln 3 x ) ^ { 2 } d x$ .
A) $x \left[ 2 - 2 \ln ( 3 x ) + ( \ln 3 x ) ^ { 2 } \right] + C$
B) $x \left[ 2 \ln ( 3 x ) + ( \ln 3 x ) ^ { 2 } \right] + C$
C) $3 x \left[ 2 + 2 \ln ( 3 x ) + ( \ln 3 x ) ^ { 2 } \right] + C$
D) $x [ 2 - 2 \ln ( 3 x ) - ( \ln 3 x ) ] ^ { 2 } + C$
E) $3 x [ 2 \ln ( 3 x ) + ( \ln 3 x ) ] ^ { 2 } + C$

Question

Quizplus · Accepted Answer

The correct integral of $\int ( \ln 3 x ) ^ { 2 } d x$ can be found using integration by parts or a table of integrals, leading to the formula $x \left[ (\ln x)^2 - 2\ln x + 2 \right]$ after adjusting for the constant 3 inside the logarithm. The answer that matches this form, after considering the properties of logarithms, is option A: $x \left[ 2 - 2 \ln ( 3 x ) + ( \ln 3 x ) ^ { 2 } \right] + C$.

Use a Table of Integrals to Find the Indefinite Integral ∫(ln⁡3x)2dx\int ( \ln 3 x ) ^ { 2 } d x∫(ln3x)2dx

Use a Table of Integrals to Find the Indefinite Integral $\int ( \ln 3 x ) ^ { 2 } d x$