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) \(\frac { x } { 2 } - \frac { 3 } { 4 } \ln | 2 x + 3 | + C\)

---

Definitions:

Discrimination

Discriminatory behavior towards individuals based on their race, age, or sex, manifesting as prejudice and unfairness.

Prejudice

A preconceived opinion or judgment formed without adequate grounds or before sufficient knowledge.

Behavior

The actions or reactions of an individual, usually in relation to the environment, which can be observed and measured externally.

Prejudice

Preconceived opinions or judgments towards people or groups without sufficient knowledge, often based on stereotypes.