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