A) B) C) D) E)

question 49

Multiple Choice

$\text { Use substitution to find the integral } \int \frac { e ^ { x } } { \left( e ^ { 2 x } + 1 \right) \left( e ^ { x } - 3 \right) } d x \text {. }$

• A)
• \(\int \frac { e ^ { x } } { \left( e ^ { 2 x } + 3 \right) \left( e ^ { x } - 3 \right) } d x = \frac { 1 } { 24 } \left( \arctan \left( e ^ { x } \right) \right) + C\)
• B)
• \(\int \frac { e ^ { x } } { \left( e ^ { 2 x } + 3 \right) \left( e ^ { x } - 3 \right) } d x = \frac { 1 } { 24 } \left( \ln \left| e ^ { 2 x } + 3 \right| - 2 \arctan \left( e ^ { x } \right) \right) + C\)
• C)
• \(\int \frac { e ^ { x } } { \left( e ^ { 2 x } + 3 \right) \left( e ^ { x } - 3 \right) } d x = \frac { 1 } { 24 } \left( 2 \ln \left| e ^ { x } - 3 \right| - \ln \left| e ^ { 2 x } + 6 \right| - 4 \arctan \left( e ^ { 2 x } \right) \right) + C\)
• D)
• \(\int \frac { e ^ { x } } { \left( e ^ { 2 x } + 3 \right) \left( e ^ { x } - 3 \right) } d x = \frac { 1 } { 20 } \left( 2 \ln \left| e ^ { x } - 3 \right| - \ln \left| e ^ { 2 x } + 1 \right| - 6 \arctan \left( e ^ { x } \right) \right) + C\)
• E)
• \(\int \frac { e ^ { x } } { \left( e ^ { 2 x } + 3 \right) \left( e ^ { x } - 3 \right) } d x = \frac { 1 } { 24 } \left( 2 \ln \left| e ^ { 2 x } - 6 \right| - \ln \left| e ^ { 2 x } + 6 \right| - 2 \arctan \left( e ^ { x } \right) \right) + C\)

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