Evaluate the Integral by Making a Substitution and Then Using $$\int \frac { e ^ { 2 x } } { 2 e ^ { x } + 3 } d x$$

question 371

Multiple Choice

Evaluate the integral by making a substitution and then using a table of integrals.
- $$\int \frac { e ^ { 2 x } } { 2 e ^ { x } + 3 } d x$$

• A) \(\frac { e ^ { x } } { 2 } + \frac { 3 } { 4 } \sin ^ { - 1 } \left| 2 e ^ { x } + 3 \right| + C\)
• B) \(\frac { 3 } { 2 e ^ { x } + 3 } + \ln \left| 2 e ^ { x } + 3 \right| + C\)
• C) \(\frac { e ^ { x } } { 2 } - \frac { 3 } { 4 } \ln \left| 2 e ^ { x } + 3 \right| + C\)
• D) \(\frac { x } { 2 } - \frac { 3 } { 4 } \ln | 2 x + 3 | + C\)

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