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Math Help - e^x integral

  1. #1
    Senior Member polymerase's Avatar
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    e^x integral

    Find \int \frac{1+e^x}{1-e^x}

    Thanks!
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Quote Originally Posted by polymerase View Post
    Find \int \frac{1+e^x}{1-e^x}
    \int {\frac{{1 + e^x }}<br />
{{1 - e^x }}\,dx} = \int {\frac{{1 - e^x + 2e^x }}<br />
{{1 - e^x }}\,dx} = \int {dx} - 2\int {\frac{{\left( {1 - e^x } \right)'}}<br />
{{1 - e^x }}\,dx}.

    So \int {\frac{{1 + e^x }}<br />
{{1 - e^x }}\,dx}=x - 2\ln \left| {1 - e^x } \right| + k.
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