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Thread: Integration Question

  1. #1
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    Integration Question

    I'm wondering how I can integrate y/(1 + y^2) ... I'm sure there is some trick to doing this but I can't figure it out at the moment.
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  2. #2
    Super Member PaulRS's Avatar
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    I guess it's $\displaystyle \int{\frac{y}{1+y^2}dy}$ isn't it?

    See it this way:$\displaystyle \int{\frac{y}{1+y^2}dy}=\frac{1}{2}\cdot{\int{\fra c{(1+y^2)'}{1+y^2}dy}}$

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  3. #3
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    More generally:

    $\displaystyle \int {\frac{{f'(x)}}
    {{f(x)}}\,dx} = \ln \left| {f(x)} \right|+k\,,\forall f(x) \ne 0$

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  4. #4
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    Quote Originally Posted by PaulRS View Post
    I guess it's $\displaystyle \int{\frac{y}{1+y^2}dy}$ isn't it?

    See it this way:$\displaystyle \int{\frac{y}{1+y^2}dy}=\frac{1}{2}\cdot{\int{\fra c{(1+y^2)'}{1+y^2}dy}}$

    So, the answer would be 1/2 * ln|1 + y^2| ??

    I suppose that works now that I works backwards and derive it. Still, that's a pretty tricky question to ask. =/ Thanks guys!
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  5. #5
    Math Engineering Student
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    Yes.

    --

    You can remove the bars 'cause $\displaystyle 1+y^2$ is always positive.
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