Evaluate the Integral $\int e^{t} \sqrt{25-e^{2 t}} d t$ A) $25 \arcsin \left(\frac{e^{t}}{5}\right)+\frac{1}{2} \sqrt{25-e^{2 t}}+C$

question 37

Multiple Choice

Evaluate the integral. $\int e^{t} \sqrt{25-e^{2 t}} d t$

• A) \(25 \arcsin \left(\frac{e^{t}}{5}\right)+\frac{1}{2} \sqrt{25-e^{2 t}}+C\)
• B) \(\frac{25}{2} \arcsin \left(\frac{e^{2 t}}{5}\right)+\frac{1}{2} \sqrt{5-e^{2}}+C\)
• C) \(\arcsin \left(\frac{e^{t}}{5}\right)+25 e^{t} \sqrt{25-e^{2 t}}+C\)
• D) \(\arcsin \left(\frac{e^{t}}{5}\right)-\frac{1}{2} \sqrt{25-e^{2 t}}+C\)
• E) \(\frac{25}{2}\) \(\arcsin \left(\frac{e^{t}}{5}\right)+\frac{1}{2} e^{t} \sqrt{25-e^{2 t}}+C\)

---

Definitions:

Humankind

The human race considered collectively, emphasizing the shared qualities and experiences of all humans.

Sociological Perspective

An approach to understanding human behavior by placing it within its broader social context.

Berger

Refers to sociologist Peter L. Berger, known for his work in the sociology of knowledge, religion, and his contribution to social constructionism.

Sociologists

Scholars or professionals who study the development, structure, and functioning of human society and the behavior of individuals in social groups.