I want to compute the following integral:

    Ro = 8
    bo = -2.68*Pi/180
    lo = 1.50*Pi/180
    r = Sqrt[Ro^2 + (Dl*Cos[bo])^2 - 2 Ro*Dl^Cos[bo]*Cos[lo]]
    z = Dl*Sin[bo]
    sa = Sqrt[(0.6^2*r^2 + z^2)/0.4^2]
    sb = ((r/0.9)^4 + (z/0.4^2)^4)^(1/4)
    rhoBulge = rhoBB*(sa^(-1.85)*Exp[-sa] + Exp[-sb^2/2])
    Integrate[rhoBulge*Dl*(1 - Dl/Ds), {Dl, 0, Ds}]

But I just obtain the integral rewritten and no solution. I'm new in mathematica, so any tip or help would be awesome. Thanks!


Your integral is very unlikely to exist in terms of elementary functions. In particular, it involves terms of the form $$ \int\exp\left[-\frac12\sqrt{a\, \text{poly}(\xi)+b \xi^{0.998906}}\right]\text d\xi, $$ which is very unfriendly as regards symbolic integration. Note that in general symbolic integration is not possible; do you have some specific reason to suspect that it will be in this case?

If what you want is a numeric answer, then you should specify numeric values for Ds and, less importantly, rhoBB. Once you do that, you can use NIntegrate to perform the integral numerically and get a numerical answer. If you want to vary Ds as a variable you can define a new function along the lines of

f[Ds_?NumericQ]:=NIntegrate[ ... ]

which you can then use for e.g. plotting.

  • $\begingroup$ Or the OP could use ParametricNDSolveValue[ y'[Dl] == rhoBulge*Dl*(1 - Dl/Ds), y, {Dl, 0, Ds}, {Ds}], perhaps. $\endgroup$ – Michael E2 Jul 10 '14 at 15:26
  • $\begingroup$ Thanks Michael!!! I will try 'ParametricNDSolveValue[ y'[Dl] == rhoBulge*Dl*(1 - Dl/Ds), y, {Dl, 0, Ds}, {Ds}]'. I need the integral in terms of Ds to insert it in another integral ¬¬ $\endgroup$ – M2689 Jul 10 '14 at 18:27

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