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Express the Integrand as a Sum of Partial Fractions and Evaluate

Question 2

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- 4x4+36x2+72x(x2+6) 2dx\int \frac { 4 x ^ { 4 } + 36 x ^ { 2 } + 72 } { x \left( x ^ { 2 } + 6 \right) ^ { 2 } } d x


A) 2lnx+lnx2+64x2+6+C2 \ln | x | + \ln \left| x ^ { 2 } + 6 \right| - \frac { 4 } { x ^ { 2 } + 6 } + C
B) 2lnx4x2+6+C2 \ln | x | - \frac { 4 } { x ^ { 2 } + 6 } + C
C) 2lnx+lnx2+6+C2 \ln | x | + \ln \left| x ^ { 2 } + 6 \right| + C
D) 8lnx+lnx2+6+C8 \ln | x | + \ln \left| x ^ { 2 } + 6 \right| + C

Correct Answer:

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