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Integral Mathematica

  1. May 13, 2014 #1

    ChrisVer

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    Gold Member

    Could someone please help me evaluate the integral with mathematica

    [itex] \int \frac{dx}{(a(1+x^{-1})+b(1+x^{2})-1)^{1/2}} [/itex]

    For better in your code the integral must be:
    1/sqrt[a(1+(1/x))+b(1+x^(2))-1]

    For [itex]a≤1[/itex] and for cases:

    A)[itex]0<b<1[/itex]
    B)[itex]b>1[/itex]

    I am sorry,but I haven't been able to receive mathematica yet... *sad face*
    Deep thanks in regard

    *not to be misunderstood that I'm asking to find everything ready I even know the codes I'd use in such a case:
    Expand[Assuming[0<a<1 && b>1, Integrate[1/sqrt[a(1+(1/x))+b(1+x^(2))-1]]]]
    Expand[Assuming[0<a<1 && 0<b<1, Integrate[1/sqrt[a(1+(1/x))+b(1+x^(2))-1]]]]
    (if there would be an error I'd try to remove the expand)...I just still don't have the software at hand
     
    Last edited: May 13, 2014
  2. jcsd
  3. May 13, 2014 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    I don't understand your statement that you " haven't been able to receive mathematica yet...". Does that mean that you have placed an order to buy Mathematica but it has not arrived yet, or what?

    Anyway, I don't have access to Mathematica, so I did it in Maple instead. The results are exceedingly complicated, involving Elliptic functions of complex arguments, etc. Here is the code and result for 0 < b < 1:
    > lprint(f); <---I call your function 'f'
    1/(a*(1+1/x)+b*(1+x^2)-1)^(1/2)
    J1:=int(f,x) assuming a<1,b>0,b<1: <---output suppressed by ending in ':'
    lprint(J1);-4*(EllipticF(6^(1/2)*((3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)/(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b))^(1/2),((-3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+3*12^(1/3)*b*a+3*12^(1/3)*b^2-3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)*(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(-((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+12^(1/3)*b*a+12^(1/3)*b^2-12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b))^(1/2))-EllipticPi(6^(1/2)*((3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)/(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b))^(1/2),(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b),((-3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+3*12^(1/3)*b*a+3*12^(1/3)*b^2-3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)*(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(-((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+12^(1/3)*b*a+12^(1/3)*b^2-12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b))^(1/2)))/((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)*(-(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b)*(12*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)+12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-b*12^(2/3)*a-12^(2/3)*b^2+12^(2/3)*b+I*3^(1/2)*12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(2/3)*b*a+I*3^(1/2)*12^(2/3)*b^2-I*3^(1/2)*12^(2/3)*b)/(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b))^(1/2)*((((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b)*(12*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)+12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-b*12^(2/3)*a-12^(2/3)*b^2+12^(2/3)*b-I*3^(1/2)*12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-I*3^(1/2)*12^(2/3)*b*a-I*3^(1/2)*12^(2/3)*b^2+I*3^(1/2)*12^(2/3)*b)/(-((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+12^(1/3)*b*a+12^(1/3)*b^2-12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b))^(1/2)*(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b)^2*((3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)/(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b))^(1/2)*(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)*x*((a*x+a+b*x+b*x^3-x)/x)^(1/2)/(x*(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b)*(12*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)+12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-b*12^(2/3)*a-12^(2/3)*b^2+12^(2/3)*b-I*3^(1/2)*12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-I*3^(1/2)*12^(2/3)*b*a-I*3^(1/2)*12^(2/3)*b^2+I*3^(1/2)*12^(2/3)*b)*(12*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)+12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-b*12^(2/3)*a-12^(2/3)*b^2+12^(2/3)*b+I*3^(1/2)*12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(2/3)*b*a+I*3^(1/2)*12^(2/3)*b^2-I*3^(1/2)*12^(2/3)*b)/(-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2)))^(1/2)/(3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(x*(a*x+a+b*x+b*x^3-x))^(1/2)

    Something similar is obtained for the case b > 1.

    Note: the command 'lprint' gives AASCII output suitable for inclusion as text. The on-screen output looks much better, but still needs 9 pages to display.
     
  4. May 13, 2014 #3

    ChrisVer

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    Gold Member

    Could your program then, instead, find solution to:
    [itex]a(x+1)+b(x^3+x)-x=0 [/itex]
    a(x+1)+b(x^3+x)-x=0
    for the same domains of a,b?

    (Also for the mathematica, I'm having it offered by my univ, but unfortunately I learned today that I have to send a mail first to them in order to be able to download it.)
     
  5. May 13, 2014 #4

    Mark44

    Staff: Mentor

    Questions about integrals should be posted in the Calculus & Beyond section.
     
  6. May 13, 2014 #5

    Ray Vickson

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    Yes, Maple can solve that equation---it just uses standard formulas for the solutions of a cubic equation, that you can find easily on-line. You can solve the equation yourself using Wolfram Alpha, which is like Mathematica lite and is freely available on the web. PF rules forbid me from writing the answer here.
     
  7. May 13, 2014 #6

    SammyS

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    Staff Emeritus
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    Hey Ray:

    I think there's a mistake in line 57, the 31's chara...

    Oh! Nevermind.

    I had the wrong eyeglasses on.
     
  8. May 13, 2014 #7
    tell me about your post details.

    Dear,
    Would you tell me about your thread details. I want to clear that. Thank you for your post.
     
  9. May 13, 2014 #8

    ChrisVer

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    Nevermind I'm getting weird results... For example I was expecting the cubic expression I gave above not to have positive solutions in this domains.
    However [itex]a=0.25=b[/itex] have solution at [itex]1[/itex] and [itex]0.618[/itex]...
     
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