Recent content by Wu Xiaobin

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    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    Oh my god! I feel terribly sorry for all of my friends. I regret for posting the wrong integral in the previous post. Especially for Ray Vickson. Thank you so much for your persistence. Again please accept my sincere apology for giving the wrong equation. -- Best regards Jacky Wu
  2. W

    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    Thanks for your reply. Actually I don't know where the problem is? But the result of f(\xi) appears in several academic papers. I will check it later to find out which one suits better and try to find out the exact problem.
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    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    Thank you so much for all friends who replied. I think I have worked it out, but maybe using another way to solve it. However partial fractions really help when I solve this problem. I needs great effort to type the integration process here, so I decide to attach the pdf document here...
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    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    You are right. The result is displayed in post #9. Last night I worked it out with your kind help. I would posted here later. It would take me a little time to check.
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    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    Yeah, I see. If I strive to work it out in partial fraction, I believe the result would be messy. However I have tried another method and it works out. I would post here later.
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    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    That is fine.
  7. W

    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    But how can I use \alpha,\beta without taking its real form into consideration. Just as I put in the previous message, it has quite complicate form. I am not very good at it, could you show me just how to use \alpha,\beta to obtain the partial fraction. Of course I will solve the integration...
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    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    I put the result f(\xi_1) here but I am not able to obtain f(\xi_1). The question is I can't obtain f(\xi_1) from integrating f(\xi_1,\xi_2) with respect to \xi_2 I found it too difficult to obtain the partial fractions and it's hard to integrate to obtain f(\xi) in the form I put.
  9. W

    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    I got the result as follows, but I still can't work it out. I hope if anyone could help. f(\xi_1)=\frac{(1-\eta_1\xi_1)(1-\eta_1^2-\eta_2^2-\eta_3^2)}{2[(1-\eta_1\xi_1)^2-(\eta_2^2+\eta_3^2)(1-\xi_1^2)]^{3/2}} where the domain of integration is -1\leq \xi_1\leq 1
  10. W

    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    Excuse me. I wonder you may neglect the square in the integral?
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    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    Thank you so much for your further reply. However when I work it out in Mathematica, the root appears rather complicated. Two of the roots are...
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    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    Could you please give some more hint. I am confused about using partial fractions.
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    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    Thanks for your reply, I will have a try.
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    Integral containing 1/(a+b*x+c*sqrt(d-x^2))^2

    Thank you so much if anyone can solve this integral to obtain its individual marginal PDF. The joint probability density function shows as follows...
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    Graduate Integral of complicated exponential functions

    I think you maybe right,not every integral can be expressed in classical functions.Maybe approximation is the only way to obtain the result.I will try to expand the integrand into series to see whether i can make a approximation.