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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!

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1 Answer 1

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.

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Or the OP could use ParametricNDSolveValue[ y'[Dl] == rhoBulge*Dl*(1 - Dl/Ds), y, {Dl, 0, Ds}, {Ds}], perhaps. –  Michael E2 Jul 10 at 15:26
    
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 ¬¬ –  M2689 Jul 10 at 18:27

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