I’ve been experimenting/playing with the Rubi package for MMA, see here. Unfortunately I have not been able to find too much documentation.

For the following function of c I was surprised MMA returned an answer, while Rubi returned… well I don’t quite know how to interpret what was produced. I’d appreciate any light you can shed

fc = -(1/2) Erf[((2 m - k^2) - 2 Log[c + b] + 2 Log[a])/(2 Sqrt[2] k)] - 1/2  fcresmma =   Assuming[m \[Element] Reals && k > 0 && c >= 0 && a > 0 && b > 0,    Integrate[fc, c]]  fcres = Assuming[   m \[Element] Reals && k > 0 && c >= 0 && a > 0 && b > 0, Int[fc, c]] 

The MMA (11.2) results is

1/2 (-c - (b + c) Erf[(-k^2 + 2 m + 2 Log[a] - 2 Log[b + c])/( 2 Sqrt[2] k)] +  a E^m Erf[(k^2 + 2 m + 2 Log[a] - 2 Log[b + c])/(2 Sqrt[2] k)]) 

The Rubi result is:

-(c/2) - Dist[1/2, Subst[ Int[ Erf[        (-k^2 (1 - (2 (m + Log[a]))/k^2) - 2 Log[c])/(2 Sqrt[2] k) ], c], c, b + c], c]