Evaluate the Integral $$\int \frac { ( x + 5 ) ^ { 2 } \tan ^ { - 1 } ( 2 x ) + 4 x ^ { 3 } + x } { \left( 4 x ^ { 2 } + 1 \right) ( x + 5 ) ^ { 2 } } d x$$

question 422

Multiple Choice

Evaluate the integral.
- $$\int \frac { ( x + 5 ) ^ { 2 } \tan ^ { - 1 } ( 2 x ) + 4 x ^ { 3 } + x } { \left( 4 x ^ { 2 } + 1 \right) ( x + 5 ) ^ { 2 } } d x$$

• A) \(\frac { \left( \tan ^ { - 1 } 2 x \right) ^ { 2 } } { 2 } + \ln | x + 5 | - \frac { 5 } { x + 5 } + C\)
• B) \(( x + 5 ) ^ { 2 } \tan ^ { - 1 } 2 x + \ln | x + 5 | + \frac { 5 } { x + 5 } + C\)
• C) \(\frac { \left( \tan ^ { - 1 } 2 x \right) ^ { 2 } } { 4 } + \ln | x + 5 | + \frac { 5 } { x + 5 } + C\)
• D) \(\frac { \left( \tan ^ { - 1 } 2 x \right) ^ { 2 } } { 4 } + \frac { 5 } { x + 5 } + C\)

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