# Integration - Unfamiliar

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• October 2nd 2009, 12:59 AM
madmartigano
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.
• October 2nd 2009, 01:03 AM
simplependulum
$\int \sqrt{ e^{2t} + e^{-2t} + 2} ~dt$

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

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

$= e^t - e^{-t} + C$
• October 2nd 2009, 01:09 AM
madmartigano
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.