$\text { Use integration tables to find } \int \frac { \cos ( x ) } { 4 \sin ^ { 2 } ( x ) + 5 \sin ( x ) + 4 } d x$

question 32

Multiple Choice

$\text { Use integration tables to find } \int \frac { \cos ( x ) } { 4 \sin ^ { 2 } ( x ) + 5 \sin ( x ) + 4 } d x$

• A) \(\frac { 1 } { 8 } \left( \ln \left| 4 + 5 \sin ( x ) + 4 \sin ^ { 2 } ( x ) \right| - \frac { 10 } { \sqrt { 39 } } \arctan \left( \frac { 8 \sin ( x ) + 5 } { \sqrt { 39 } } \right) \right) + C\)
• B) \(\frac { 2 } { \sqrt { 39 } } \arctan \left( \frac { 8 \cos ( x ) + 5 } { \sqrt { 39 } } \right) + C\)
• C) \(\frac { 1 } { \sqrt { 39 } } \ln \left| \frac { 8 \sin ( x ) + 5 - \sqrt { 39 } } { 8 \sin ( x ) + 5 + \sqrt { 39 } } \right| + C\)
• D) \(\frac { 2 } { \sqrt { 39 } } \arctan \left( \frac { 8 \sin ( x ) + 5 } { \sqrt { 39 } } \right) + C\)
• E)\(\frac { 1 } { \sqrt { 39 } } \ln \left| \frac { 8 \cos ( x ) + 5 - \sqrt { 39 } } { 8 \cos ( x ) + 5 + \sqrt { 39 } } \right| + C\)