I want to calculate this Integral to solve one important differential equation in general relativity [closed]

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开发者_如何学Python

Closed 12 years ago.

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∫▒fdf/√(f(f^3 a+6bf+3c)) a, b, c are constant

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The program is:

 Integrate[x/Sqrt[x (x^3 a + 6 b x + 3 c )], x]

As per Mathematica output:

(2*(EllipticF[ArcSin[Sqrt[(x*(-R[1] + R[3]))/((x - R[1])*R[3])]], 
                             ((R[1] - R[2])*R[3])/(R[2]*(R[1] - R[3]))] -       
    EllipticPi[R[3]/(-R[1] + R[3]), 
             ArcSin[Sqrt[(x*(-R[1] + R[3]))/((x - R[1])*R[3])]], 

                ((R[1] - R[2])*R[3])/(R[2]*(R[1] - R[3]))])*(x - R[1])^2*

                Sqrt[(R[1]*(x - R[2]))/((x - R[1])*R[2])]*R[3]*
                Sqrt[x*R[1]*(x - R[3])*(-R[1] + R[3]^2)])/
               (Sqrt[x*(3*c + 6*b*x + a*x^3)]* (R[1] - R[3]))

Where:

         Root[n]  

Is the n root of the polynomial

         p[u]=3 c + 6 b u + a u^3  

Additionally, you may try this in Wolfram Alpha to get the indefinite integral, or definite ones. But I really think that if you are solving one important differential equation in general relativity and don't tried Mathematica and/or Wolfram Alpha, you may be a) Trolling or b) In great trouble