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

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