$\text { Use partial fractions to find the integral } \int \frac { 12 x ^ { 2 } + 5 x + 225 } { x ^ { 3 } + 25 x } d x$

question 105

Multiple Choice

$\text { Use partial fractions to find the integral } \int \frac { 12 x ^ { 2 } + 5 x + 225 } { x ^ { 3 } + 25 x } d x$

• A) \(9 \ln | x | + ( 3 x + 5 ) \ln \left( x ^ { 2 } + 25 \right) + C\)
• B) \(9 \ln | x | + 3 \ln | x + 5 | + 5 \ln | x - 5 | + C\)
• C) \(9 \ln | x | + \frac { 3 } { 2 } \ln \left( x ^ { 2 } + 25 \right) + \arctan \left( \frac { x } { 5 } \right) + C\)
• D) \(9 \ln | x | + \frac { 3 } { 2 } \ln \left( x ^ { 2 } + 25 \right) + C\)
• E) \(237 \ln | x | - \frac { 5 } { x } + C\)

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