Evaluate the Integral $$\int \frac { e ^ { 3 \theta } } { 1 + e ^ { 3 \theta } } d \theta$$

question 50

Multiple Choice

Evaluate the integral.
- $$\int \frac { e ^ { 3 \theta } } { 1 + e ^ { 3 \theta } } d \theta$$

• A) \(3 \ln \left( 1 + e ^ { 3 \theta } \right) + C\)
• B) \(\frac { \ln \left( 1 + e ^ { 3 \theta } \right) } { 3 } + C\)
• C) \(\frac { \ln \left( 1 + 3 e ^ { \theta } \right) } { 3 } + C\)
• D) \(\ln \left( 1 + \mathrm { e } ^ { 3 \theta } \right) + C\)

---

Definitions:

Economic Profit

The split between a firm's entire proceeds and its total disbursements, embracing both acknowledged and veiled costs.

Normal Profit

The minimum profit necessary for a company to remain competitive in the market, equating to the opportunity cost of the resources employed.

Normal Profit

The minimum level of profit necessary for a company to remain competitive in the market, often considered the break-even point.

Marginal Cost

Marginal cost is the increase in total cost that arises from producing one more unit of a good or service. It is a critical concept in economics for decision-making regarding production levels.