public override Algebraic Integrate(Variable v)
{
if (!den.Depends(v))
{
return(nom.Integrate(v) / den);
}
var quot = den.Derive(v) / nom;
if (quot.Derive(v).Equals(Symbol.ZERO))
{
return(FunctionVariable.Create("log", den) / quot);
}
var q = new[] { nom, den };
Poly.polydiv(q, v);
if (q[0] != Symbol.ZERO && nom.IsRat(v) && den.IsRat(v))
{
return(q[0].Integrate(v) + (q[1] / den).Integrate(v));
}
if (IsRat(v))
{
Algebraic r = Symbol.ZERO;
var h = Horowitz(nom, den, v);
if (h[0] is Rational)
{
r = r + h[0];
}
if (h[1] is Rational)
{
r = r + new TrigInverseExpand().SymEval((( Rational )h[1]).intrat(v));
}
return(r);
}
throw new SymbolicException("Could not integrate Function " + this);
}