Find the integral.
$\int \frac { d x } { x ( x - 3 ) }$
A) $\frac { 1 } { 3 } \ln \left| \frac { x - 3 } { x } \right| + C$
B) $\frac { 1 } { 3 } \ln \left| \frac { x ^ { 2 } - 3 } { x } \right| + C$
C) $3 \ln \left| \frac { x ^ { 2 } - 3 } { x } \right| + C$
D) $3 \ln \left| \frac { x - 3 } { x } \right| + C$

Question

Quizplus · Accepted Answer

We can use partial fraction decomposition to write $\frac{1}{x(x-3)}$ as $\frac{1}{3x} - \frac{1}{3(x-3)}$. Thus, we have:
\begin{align*}
\int \frac{dx}{x(x-3)} &= \int \left(\frac{1}{3x} - \frac{1}{3(x-3)}ight)dx \
&= \frac{1}{3} \ln\left|\frac{x}{x-3}ight| + C \
&= \frac{1}{3} \ln\left|\frac{x-3}{x}ight| + C &&	ext{(using log property)}
\end{align*}
Therefore, the best choice is $\boxed{	ext{(A)}}$.

Find the Integral ∫dxx(x−3)\int \frac { d x } { x ( x - 3 ) }∫x(x−3)dx​

Find the Integral $\int \frac { d x } { x ( x - 3 ) }$