How could this be integrated?

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

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

Any help will be appreciated.

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- Oct 1st 2009, 11:59 PMmadmartiganoIntegration - Unfamiliar
How could this be integrated?

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

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

Any help will be appreciated. - Oct 2nd 2009, 12:03 AMsimplependulum
$\displaystyle \int \sqrt{ e^{2t} + e^{-2t} + 2} ~dt$

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

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

$\displaystyle = e^t - e^{-t} + C$ - Oct 2nd 2009, 12:09 AMmadmartigano
Thank you. How did you get from

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

to

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

$ ?

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