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 write the given integral as
$$\int \frac{1}{x} dx - \int \frac{1}{x-3} dx$$
Solving each integral separately, we get
$$\ln |x| - \ln |x-3| + C = \ln \left|\frac{x-3}{x}\right| + C = \frac{1}{3} \ln \left|\frac{x-3}{x}\right| + C'$$
Therefore, the correct choice is A.

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

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