# Math Help - Integration - Unfamiliar

1. ## Integration - Unfamiliar

How could this be integrated?

$\int {\sqrt {{e^{2t}} + {e^{ - 2t}} + 2} } dt$

I vaguely remember using logs to help integrate (or maybe differentiate), but I'm at a loss here.

Any help will be appreciated.

2. $\int \sqrt{ e^{2t} + e^{-2t} + 2} ~dt$

$= \int \sqrt{ ( e^t + e^{-t})^2}~dt$

$= \int [e^t + e^{-t} ]~dt$

$= e^t - e^{-t} + C$

3. Thank you. How did you get from

${{e^{2t}} + {e^{ - 2t}} + 2}$

to

${\left( {{e^t} + {e^{ - t}}} \right)^2}
$
?

Edit: Nevermind, I wrote it out. Thank you again.