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Math Help - exponential function integral...

  1. #1
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    exponential function integral...

    evaluate this integral from [0,1]

    int[[(e^(2x)-e^(-2x))/(e^(2x)+e^(-2x)]dx]

    btw, could someone point me towards the info on how to format these correctly?
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  2. #2
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    Quote Originally Posted by thedoge View Post
    evaluate this integral from [0,1]

    int[[(e^(2x)-e^(-2x))/(e^(2x)+e^(-2x)]dx]

    btw, could someone point me towards the info on how to format these correctly?
    This is a hyperbolic tangent, no?

    \int \tanh 2xdx=\frac{1}{2}\ln (\cosh 2x)+C
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  3. #3
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    Hello, thedoge!

    Evaluate: . \int^1_0\frac{e^{2x} - e^{-2x}}{e^{2x} + e^{-2x}}\,dx

    Did you notice that the numerator is almost the derivative of the denominator?

    Let u \:=\:e^{2x} + e^{-2x}\quad\Rightarrow\quad du \:=\:\left(2e^{2x} - 2e^{-2x}\right)\,dx \:=\:2\left(e^{2x} - e^{-2x}\right)\,dx

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