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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

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

Evaluate the Integral ∫et25−e2tdt\int e^{t} \sqrt{25-e^{2 t}} d t∫et25−e2t​dt A) 25arcsin⁡(et5)+1225−e2t+C25 \arcsin \left(\frac{e^{t}}{5}\right)+\frac{1}{2} \sqrt{25-e^{2 t}}+C25arcsin(5et​)+21​25−e2t​+C

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

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