Evaluate the Integral $\int _ { 1 } ^ { 2 } x \ln ( 5 x ) \mathrm { d } x$

Evaluate the integral. $\int _ { 1 } ^ { 2 } x \ln ( 5 x ) \mathrm { d } x$

A) $\frac { 3 \ln 5 } { 2 } - \frac { 3 } { 4 }$
B) $2 \ln 10 - \frac { \ln 5 } { 2 } - \frac { 3 } { 4 }$
C) $2 \ln 10 - \frac { 3 \ln 5 } { 2 } - \frac { 15 } { 4 }$
D) $- \ln 100 + \frac { \ln 5 - 1 } { 2 }$
E) $\ln 100 + \frac { \ln 5 + 1 } { 2 }$

Correct Answer:

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