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Math Help - Integration - Unfamiliar

  1. #1
    Newbie madmartigano's Avatar
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    Merced, California
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    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.
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  2. #2
    Super Member
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     \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
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  3. #3
    Newbie madmartigano's Avatar
    Joined
    Mar 2009
    From
    Merced, California
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    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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