Evaluate the Integral by First Performing Long Division on the Integrand

question 103

Multiple Choice

Evaluate the integral by first performing long division on the integrand and then writing the proper fraction as a sum of partial fractions.
- $$\int \frac { 3 x ^ { 4 } + 15 x ^ { 2 } + 5 } { x ^ { 3 } + 5 x } d x$$

• A) \(\frac { 3 } { 2 } x ^ { 2 } - \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 5 \right| + C\)
• B) \(\frac { 3 } { 2 } x ^ { 2 } + \ln | x | - x \ln \left| x ^ { 2 } + 5 \right| + C\)
• C) \(\frac { 3 } { 2 } x ^ { 2 } + \ln | x | + \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 5 \right| + C\)
• D) \(\frac { 3 } { 2 } x ^ { 2 } + \ln | x | - \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 5 \right| + C\)