myarctan := proc(y,x) `if`(nargs = 1, arctan(y),evalf(Pi/2)-arctan(expand(x/y))); end: myarctanh := (y) -> myln(1+y)/2 - myln(1-y)/2: myln := proc(u) local c,d,v; d := degree(u,x); c := coeff(u,x,d); v := expand(u/c); if d = 1 then v := abs(v); fi; ln(v); end: ratint := proc(f,x) local g; g := int(f,x); if has(g,{RootOf,int}) then g := int(convert(evalf(f),parfrac,x),x); fi; g := eval( subs(ln=myln,arctan = myarctan,arctanh=myarctanh, signum=1,abs=(x->x), g)); g := expand(g); if (type(g,`+`)) then g := remove((a)->type(a,constant),g); fi; g; end:

g[1] := (x) -> x^2 + x + 1 + 1/x + 1/x^2;g[2] := (x) -> 1/(x-1) + 1/(x^2-1) + 1/(x^3-1);g[3] := (x) -> 1/(x-1)^2 + 1/(x-2)^3 + 1/(x-3)^4;g[4] := (x) -> 1/(x+1) + 1/(x^2+1) + 1/(x^3+1);g[5] := (x) -> x/(x+1)*(x+2)/(x+3)*(x+4);g[6] := (x) -> x/(x+1)^2*(x+2)/(x+3)^2*(x+4);g[7] := (x) -> (x^3+4*x^2+x+2)/(x-1)^2/(x+1)^3;g[8] := (x) -> 1/(x^2+8*x+1);g[9] := (x) -> (x^2+1)^(-5);g[10] := (x) -> 1/(x^8+x^2+1);

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