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I'm tring to solve the Indefinite Integral of the function:

fx[zf_] := 
 Log[1.9607843137254901` (0.42` + 
     0.09000000000000008` (0.11030501767281171` \
E^(-0.06294157608695654` (-0.38964705882352935` + zf)^2) + 
        1/2 Erfc[0.250881597744746` (-0.38964705882352935` + zf)] - 
        1/2 E^(0.0981` zf) (1.0382243764705883` + 0.0981` zf) Erfc[
          0.250881597744746` (0.38964705882352935` + zf)]))]

When I try to solve the integral:

Integrate[fx[zf], zf]

Mathematica do not give any result. The only assumptyon needed is that zf must be >= 0.

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  • 1
    $\begingroup$ There probably isn't a 'nice' closed form antiderivative. It's too complicated for Mathematica. You can get a series approximation though if that helps. Here's the first 5 terms of the series: Series[Integrate[fx[zf], zf], {zf, 0, 5}] giving -0.15174 zf - 0.00803721 zf^2 + 0.00048911 zf^3 + 0.0000386184 zf^4 - 4.66256*10^-6 zf^5 $\endgroup$ – flinty Jul 31 '20 at 22:34
  • $\begingroup$ I also attempted it with Rubi, rulebasedintegration.org but the result was extremely complicated and still contained unresolved integrals. $\endgroup$ – flinty Jul 31 '20 at 22:45
  • 1
    $\begingroup$ Sometimes exact solvers like Integrate do not work well with floating-point coefficients. Round-off error can be a problem. In this case, it seems there's no known antiderivative. NDSolve could compute a numerical antiderivative over a finite domain, if that's of interest. $\endgroup$ – Michael E2 Aug 1 '20 at 3:24

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