Evaluate the integral by first performing long division on the integrand and then writing the proper fraction as a sum of partial fractions.
-$$\int \frac { 9 x ^ { 3 } + 18 x ^ { 2 } + 12 x + 5 } { 9 x ^ { 2 } + 18 x + 9 } d x$$
A) $\frac { 1 } { 2 } x ^ { 2 } + \ln | 3 x + 3 | - \frac { 2 } { 3 x + 3 } + C$
B) $\frac { 1 } { 2 } x ^ { 2 } - \frac { 3 x + 5 } { 3 x + 3 } + C$
C) $\frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 3 } \ln | 3 x + 3 | - \frac { 2 } { 3 } \frac { 1 } { 3 x + 3 } + C$
D) $\frac { 1 } { 2 } x ^ { 2 } + \ln | 3 x + 3 | - \frac { 2 } { 3 } \frac { 1 } { 3 x + 3 } + C$

Question

Quizplus · Accepted Answer

The Answer of Evaluate the integral by first performing long division on the integrand and then writing the proper fraction as a sum of partial fractions.
-$$\int \frac { 9 x ^ { 3 } + 18 x ^ { 2 } + 12 x + 5 } { 9 x ^ { 2 } + 18 x + 9 } d x$$
A) $\frac { 1 } { 2 } x ^ { 2 } + \ln | 3 x + 3 | - \frac { 2 } { 3 x + 3 } + C$
B) $\frac { 1 } { 2 } x ^ { 2 } - \frac { 3 x + 5 } { 3 x + 3 } + C$
C) $\frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 3 } \ln | 3 x + 3 | - \frac { 2 } { 3 } \frac { 1 } { 3 x + 3 } + C$
D) $\frac { 1 } { 2 } x ^ { 2 } + \ln | 3 x + 3 | - \frac { 2 } { 3 } \frac { 1 } { 3 x + 3 } + C$

Evaluate the Integral by First Performing Long Division on the Integrand