implement integrals resulting in 2F1 and AppellF1 expressions #22650
Description
These are the rules in the Rubi integrator's chapters 1.1, 1.2, and 1.3 that result in hypergeometric or AppellF1 expressions. They could be implemented to increase coverage of the available integration libraries:
- (c+dx)n/(a+bx), n not in ZZ --> Rule 1.1.2.H.4
- (bx)m(c+dx)n, --> Rules 1.1.2.H.1.*
- (a+bx)m(c+dx)n --> Rules 1.1.2.H.2.*
- (a+bx)m(c+dx)n(e+fx)p, m+n+p+2==0 --> Rules 1.1.3.H
- (bx)m(c+dx)n(e+fx)p, m,n not in ZZ --> Rules 1.1.3.A.1.*
- (a+bx)m(c+dx)n(e+fx)p, m,n not in ZZ --> Rules 1.1.3.A.2/3.*
- (a+bx+cx2)p, 4p not in ZZ --> Rule 1.2.1.H
- (a+bxn)p, p not in ZZ, a>0 --> Rule 1.3.1.7
- (cx)m(a+bxn)p, p not in ZZ --> Rules 1.3.2.12
- (a+bxn)p(c+dxn)q, n(p+q+1)+1==0 --> Rule 1.3.3.5.4
- (ex)m(a+bxn)p(c+dxn)q, a,c>0, m!=1, m+n!=1 --> Rule 1.3.4.A.1
- (axj+bxn)p, p not in ZZ, j!=n --> Rules 1.3.8.x
- xm(axj+bxn)p, j!=n --> Rules 1.3.9.x
This could be useful even without a full #22410
Depends on #22651
Depends on #22763
Component: calculus
Issue created by migration from https://trac.sagemath.org/ticket/22650