Evaluate the Integral $$\int \frac { e ^ { 2 \theta } } { 1 + e ^ { 2 \theta } } d \theta$$

question 70

Multiple Choice

Evaluate the integral.
- $$\int \frac { e ^ { 2 \theta } } { 1 + e ^ { 2 \theta } } d \theta$$

• A) \(2 \ln \left( 1 + \mathrm { e } ^ { 2 \theta } \right) + \mathrm { C }\)
• B) \(\ln \left( 1 + \mathrm { e } ^ { 2 \theta } \right) + C\)
• C) \(\frac { \ln \left( 1 + 2 e ^ { \theta } \right) } { 2 } + C\)
• D) \(\frac { \ln \left( 1 + \mathrm { e } ^ { 2 \theta } \right) } { 2 } + \mathrm { C }\)

---

Definitions:

Insomnia

Condition characterized by chronic inability to sleep or remain asleep through the night.

Sleep deprivation

A condition resulting from inadequate quantity or quality of sleep, affecting physical, mental, and emotional health.

Irritability

A state of increased sensitivity or annoyance, often resulting from stress or discomfort.

Deep breathing

A technique that involves taking slow, deliberate breaths deep into the lungs, often used for relaxation or to improve lung function.