Evaluate the Integral $$\int \frac { ( - \sin t - 7 ) \cos t d t } { \sin ^ { 3 } t + 2 \sin ^ { 2 } t + \sin t + 2 }$$

question 281

Multiple Choice

Evaluate the integral.
- $$\int \frac { ( - \sin t - 7 ) \cos t d t } { \sin ^ { 3 } t + 2 \sin ^ { 2 } t + \sin t + 2 }$$

• A) \(- \ln | t + 2 | + \frac { 1 } { 2 } \ln \left| t ^ { 2 } + 1 \right| - 3 \tan ^ { - 1 } t + C\)
• B) \(\ln | \sin t + 2 | - \ln \left| \sin ^ { 2 } t + 1 \right| - 5 \tan ^ { - 1 } ( \sin t ) + C\)
• C) \(- \ln | \sin t + 2 | + \frac { 1 } { 2 } \ln \left| \sin ^ { 2 } t + 1 \right| - 3 \tan ^ { - 1 } ( \sin t ) + C\)
• D) \(- \ln | \sin t + 2 | + \frac { 1 } { 2 } \ln \left| \sin ^ { 2 } t + 1 \right| + C\)

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