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March 29, 2017

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evaluate integral by substitution (e^x-e^(-x))/(e^x+e^(-x))dx

  • integral calculus - ,

    Note that you have Integral(tanh(x) dx)
    = Integral (sinh(x)/cosh(x) dx)
    let u = cosh(x)
    du = sinh(x) dx

    and you have Integral(du/u) = ln(u) = ln(cosh(x)) = ln(e^x + e^-x) + C

    Equivalently, let u = e^x + e^-x
    Then du = e^x - e^-x du

    and you have du/u

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