Integration - Unfamiliar

**madmartigano** · October 1st 2009, 11:59 PM

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.

**simplependulum** · October 2nd 2009, 12:03 AM

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

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

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

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

**madmartigano** · October 2nd 2009, 12:09 AM

Thank you. How did you get from

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

to

${\left( {{e^t} + {e^{ - t}}} \right)^2}<br />$ ?

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

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