Evaluate the Integral $$\int \frac { 7 d x } { \left( x ^ { 2 } + 2 x + 2 \right) ^ { 2 } }$$

question 4

Multiple Choice

Evaluate the integral.
$$\int \frac { 7 d x } { \left( x ^ { 2 } + 2 x + 2 \right) ^ { 2 } }$$

• A) \(\frac { 1 } { 2 } \left( \tan ( x + 1 ) + \frac { 17 } { x ^ { 2 } + 2 x + 2 } \right) + C\)
• B) \(\frac { 1 } { 2 } \left( \tan ^ { - 1 } ( x + 2 ) + \frac { 7 } { x ^ { 2 } + 2 } \right) + C\)
• C) \(\frac { 1 } { 2 } \left( \tan ^ { - 1 } ( x + 7 ) + \frac { 1 } { x ^ { 2 } + 2 x + 2 } \right) + C\)
• D) \(\frac { 7 } { 2 } \left( \tan ( x + 2 ) + \frac { x + 1 } { x ^ { 2 } + 2 x + 2 } \right) + C\)
• E) \(\frac { 7 } { 2 } \left( \tan ^ { - 1 } ( x + 1 ) + \frac { x + 1 } { x ^ { 2 } + 2 x + 2 } \right) + C\)

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