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Math Help - integral method for rational functions of sinh and cosh

  1. #1
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    integral method for rational functions of sinh and cosh

    I have a feeling I should know this, but what's the method for finding the integral of functions like

    \int \frac{1}{\sinh x + 2\cosh x} \, dx

    This is easy is it were regular trigonometric functions (using the famous tan substitution) but how do we approach these one?

    No need to solve the problem, I'm just asking about the method

    Regards,

    Stonehambey
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  2. #2
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    Quote Originally Posted by Stonehambey View Post
    I have a feeling I should know this, but what's the method for finding the integral of functions like

    \int \frac{1}{\sinh x + 2\cosh x} \, dx

    This is easy is it were regular trigonometric functions (using the famous tan substitution) but how do we approach these one?

    No need to solve the problem, I'm just asking about the method

    Regards,

    Stonehambey
    The first thing I'd do is replace the hyperbolic functions with their exponential definitions.


    Alternatively, you could probably use the less famous tanh substitution.
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    tanh substitution? I've never heard of that one before.
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    Quote Originally Posted by Stonehambey View Post
    tanh substitution? I've never heard of that one before.
    Well, I did say it was less famous. It's in here: 4.
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