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Express the Integrand as a Sum of Partial Fractions and Evaluate

Question 222

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- 2x2+x+1(x2+3) (x5) dx\int \frac { 2 x ^ { 2 } + x + 1 } { \left( x ^ { 2 } + 3 \right) ( x - 5 ) } d x


A) 2lnx5+33tan1(x33) +C2 \ln | x - 5 | + \frac { \sqrt { 3 } } { 3 } \tan ^ { - 1 } \left( \frac { x \sqrt { 3 } } { 3 } \right) + C
B) 2lnx5+13tan1(x3) +C2 \ln | x - 5 | + \frac { 1 } { 3 } \tan ^ { - 1 } \left( \frac { x } { 3 } \right) + C
C) 2lnx5+tan1(x33) +C2 \ln | x - 5 | + \tan ^ { - 1 } \left( \frac { x \sqrt { 3 } } { 3 } \right) + C
D) lnx5+33tan1(x33) +C\ln | x - 5 | + \frac { \sqrt { 3 } } { 3 } \tan ^ { - 1 } \left( \frac { x \sqrt { 3 } } { 3 } \right) + C

Correct Answer:

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