public Algebraic integrate(Variable var) throws JasymcaException {
Algebraic in = Zahl.ZERO;
for (int i = 1; i < coef.length; i++) {
if (!coef[i].depends(var))
if (var.equals(this.var))
// c*x^n -->1/(n+1)*x^(n+1)
in = in.add(coef[i].mult(new Polynomial(var).pow_n(i + 1).div(new Unexakt(i + 1))));
else if (this.var instanceof FunctionVariable
&& ((FunctionVariable) this.var).arg.depends(var))
// f(x)
if (i == 1) in = in.add(((FunctionVariable) this.var).integrate(var).mult(coef[1]));
// (f(x))^2, (f(x))^3 etc
// give up here but try again after exponential normalization
else throw new JasymcaException("Integral not supported.");
else
// Constant: c --> c*x
in = in.add(coef[i].mult(new Polynomial(var).mult(new Polynomial(this.var).pow_n(i))));
else if (var.equals(this.var))
// c(x)*x^n , should not happen if this is canonical
throw new JasymcaException("Integral not supported.");
else if (this.var instanceof FunctionVariable
&& ((FunctionVariable) this.var).arg.depends(var)) {
if (i == 1 && coef[i] instanceof Polynomial && ((Polynomial) coef[i]).var.equals(var)) {
// poly(x)*f(x)
// First attempt: try to isolate inner derivative
// poly(x)*f(w(x)) --> check poly(x)/w' == q : const?
// yes --> Int f dw * q
p("Trying to isolate inner derivative " + this);
try {
FunctionVariable f = (FunctionVariable) this.var;
Algebraic w = f.arg; // Innere Funktion
Algebraic q = coef[i].div(w.deriv(var));
if (q.deriv(var).equals(Zahl.ZERO)) { // q - constant
SimpleVariable v = new SimpleVariable("v");
Algebraic p = FunctionVariable.create(f.fname, new Polynomial(v));
Algebraic r = p.integrate(v).value(v, w).mult(q);
in = in.add(r);
continue;
}
} catch (JasymcaException je) {
// Didn't work, try more methods
}
p("Failed.");
// Some partial integrations follow. To
// avoid endless loops, we flag this section
// Coefficients of coef[i] must not depend on var
for (int k = 0; k < ((Polynomial) coef[i]).coef.length; k++)
if (((Polynomial) coef[i]).coef[k].depends(var))
throw new JasymcaException("Function not supported by this method");
if (loopPartial) {
loopPartial = false;
p("Partial Integration Loop detected.");
throw new JasymcaException("Partial Integration Loop: " + this);
}
// First attempt: x^n*f(x) , n-times diff!
// works for exp,sin,cos
p("Trying partial integration: x^n*f(x) , n-times diff " + this);
try {
loopPartial = true;
Algebraic p = coef[i];
Algebraic f = ((FunctionVariable) this.var).integrate(var);
Algebraic r = f.mult(p);
while (!(p = p.deriv(var)).equals(Zahl.ZERO)) {
f = f.integrate(var).mult(Zahl.MINUS);
r = r.add(f.mult(p));
}
loopPartial = false;
in = in.add(r);
continue;
} catch (JasymcaException je) {
loopPartial = false;
}
p("Failed.");
// Second attempt: x^n*f(x) , 1-times int!
// works for log, atan
p("Trying partial integration: x^n*f(x) , 1-times int " + this);
try {
loopPartial = true;
Algebraic p = coef[i].integrate(var);
Algebraic f = new Polynomial((FunctionVariable) this.var);
Algebraic r = p.mult(f).sub(p.mult(f.deriv(var)).integrate(var));
loopPartial = false;
in = in.add(r);
continue;
} catch (JasymcaException je3) {
loopPartial = false;
}
p("Failed");
// Add more attempts....
throw new JasymcaException("Function not supported by this method");
} else throw new JasymcaException("Integral not supported.");
} else // mainvar independend of var, treat as constant and integrate coef
in = in.add(coef[i].integrate(var).mult(new Polynomial(this.var).pow_n(i)));
}
if (coef.length > 0) in = in.add(coef[0].integrate(var));
return in;
}
