Question $6(1$ point$)$

Evaluate the integral

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^t\sqrt[\phantom{2}]{169-e^{2t}}dt$

Select the correct answer.

$arcsin(\frac{e^t}{13})\frac{1}{2}{e}^t\sqrt[\phantom{2}]{160-e^{2t}}C$

$\frac{169}{2}arcsin(\frac{e^t}{13})\frac{1}{2}\sqrt[\phantom{2}]{169-e^{21}}c$

$\frac{160}{2}arcsin(\frac{t^2}{13})\frac{1}{2}e\sqrt[\phantom{2}]{160-e^2}C$

$arcsin(\frac{e^t}{13})\frac{1}{2}\sqrt[\phantom{2}]{169-e^{2t}}c$