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Math Help - integration by mathematica

  1. #1
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    integration by mathematica

    Hi Guys,

    I need to solve the following integral using mathematica, but i do not know how to identify the constants and do symbolic integration, so i get a very nasty expression .

    dw/dt=(t-r)/{(t-b)*(t-p)*sqrt((t-a)*(t-c))}

    a,b ,p,c,r are constants.

    any help with this!

    Thanks

    mopen80
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  2. #2
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    Re: integration by mathematica

    I'm not sure about the Mathematica expressions, but I'm pretty sure you can solve this using partial fractions (it won't be pretty though)...
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  3. #3
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    Re: integration by mathematica

    Quote Originally Posted by mopen80 View Post
    Hi Guys,

    I need to solve the following integral using mathematica, but i do not know how to identify the constants and do symbolic integration, so i get a very nasty expression .

    dw/dt=(t-r)/{(t-b)*(t-p)*sqrt((t-a)*(t-c))}

    a,b ,p,c,r are constants.

    any help with this!

    Thanks

    mopen80
    $$\frac{dw}{dt}=\frac{t-r}{(t-b)(t-p)\sqrt{(t-a)(t-c)}}$$

    The output from Mathematica is

    $$\int \frac{t-r}{(t-b) (t-p) \sqrt{(t-a) (t-c)}} \, dt=$$

    $$\frac{\sqrt{t-a} \sqrt{t-c} \left(i \sqrt{a-p} (b-r) \sqrt{c-p} \log \left(\frac{i (b-p) \left(a (b-2 c+t)+2 i \sqrt{a-b} \sqrt{t-a} \sqrt{b-c} \sqrt{t-c}+b (c-2 t)+c t\right)}{\sqrt{a-b} \sqrt{b-c} (b-r) (b-t)}\right)+\sqrt{a-b} \sqrt{b-c} (p-r) \log (p-t)+\sqrt{a-b} \sqrt{b-c} (r-p) \log \left(-a (-2 c+p+t)+2 \left(\sqrt{a-p} \sqrt{t-a} \sqrt{c-p} \sqrt{t-c}+p t\right)-c (p+t)\right)\right)}{\sqrt{a-b} \sqrt{a-p} \sqrt{b-c} (p-b) \sqrt{c-p} \sqrt{(t-a) (t-c)}}$$

    That is what it is. I don't know how you can simplify it without having values for your constants.
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  4. #4
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    Re: integration by mathematica

    Thanks

    I got this expression already in Mathematica.Any guidelines to solve this using partial fraction then?

    Thanks
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