# Indefinite Integral not Solving

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.

• 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 – flinty Jul 31 '20 at 22:34
• I also attempted it with Rubi, rulebasedintegration.org but the result was extremely complicated and still contained unresolved integrals. – flinty Jul 31 '20 at 22:45
• 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. – Michael E2 Aug 1 '20 at 3:24