The integral $\int \frac { x ^ { 2 } } { x ^ { 2 } - 2 x - 3 } d x$ is

A) $\frac { 4 x - \ln | x + 1 | + 9 \ln | x - 3 | } { 4 } + C$
B) $\frac { 4 x + \ln | x + 1 | + 9 \ln | x - 3 | } { 4 } + C$
C) $\frac { 4 x + \ln | x + 1 | - 9 \ln | x - 3 | } { 4 } + C$
D) $- \frac { 4 x - \ln | x + 1 | + 9 \ln | x - 3 | } { 4 } + C$
E) $- \frac { 4 x - \ln | x - 1 | + 9 \ln | x - 3 | } { 4 } + C$

Question

The integral $\int \frac { x ^ { 2 } } { x ^ { 2 } - 2 x - 3 } d x$ is

A) $\frac { 4 x - \ln | x + 1 | + 9 \ln | x - 3 | } { 4 } + C$
B) $\frac { 4 x + \ln | x + 1 | + 9 \ln | x - 3 | } { 4 } + C$
C) $\frac { 4 x + \ln | x + 1 | - 9 \ln | x - 3 | } { 4 } + C$
D) $- \frac { 4 x - \ln | x + 1 | + 9 \ln | x - 3 | } { 4 } + C$
E) $- \frac { 4 x - \ln | x - 1 | + 9 \ln | x - 3 | } { 4 } + C$

Quizplus · Accepted Answer

The correct answer is A because the integral of $\frac { x ^ { 2 } } { x ^ { 2 } - 2 x - 3 } d x$ is $\frac { 4 x - \ln | x + 1 | + 9 \ln | x - 3 | } { 4 } + C$. This can be found by using partial fractions to decompose the integrand into $\frac { 1 } { x - 3 } - \frac { 1 } { x + 1 }$ and then integrating each term.

The Integral ∫x2x2−2x−3dx\int \frac { x ^ { 2 } } { x ^ { 2 } - 2 x - 3 } d x∫x2−2x−3x2​dx

The Integral $\int \frac { x ^ { 2 } } { x ^ { 2 } - 2 x - 3 } d x$