Evaluate the integral. $$\int 4 \left( \frac { x - 1 } { x ^ { 2 } + 2 x } \right) d x$$
A) $4 \left( \frac { 1 } { 3 } x - \frac { 1 } { 3 } \ln x \right) + C$
B) $4 \left( \frac { 3 } { 2 } \ln ( x + 2 ) - \frac { 1 } { 2 } \ln x \right) + C$
C) $- 4 \left( \frac { \sqrt { 2 } } { 2 } \arctan x \right) + C$
D) $- 4 ( \ln x - x ) + C$
E) None of these

Question

Quizplus · Accepted Answer

The integral can be solved by partial fraction decomposition, splitting the fraction into $\frac{1}{x}$ and $\frac{1}{x+2}$, and then integrating each term separately.

Evaluate the Integral ∫4(x−1x2+2x)dx\int 4 \left( \frac { x - 1 } { x ^ { 2 } + 2 x } \right) d x∫4(x2+2xx−1​)dx

Evaluate the Integral $\int 4 \left( \frac { x - 1 } { x ^ { 2 } + 2 x } \right) d x$