Integral Heston Model Finance

Any idea why the integral is not being solved ?

This is my code:

Theta= log(2)/(Vols_L)^2;                  % Mean Reversion
Omega= (Vols_L - (Vols_L)^2);              % Long Term Variance
Psi= Theta * Omega;                        % Ornstein Uhlenbeck (1')
Eta= (Vols_L)^4;                           % Vol of Vol
Correlation= 0.5;                          % Correlation with Risky Asset
 
% ~ Variables ~ 
 
Spot= log(Spot_L);
Psi= Theta * (Omega);
A= Theta * Omega;
B1= Theta + Psi - (Correlation * Eta);
B2= Theta + Psi; 
U1= 1/2;
U2= -1/2;
Element= 0;
 
% ~ Components ~
 
d1= sqrt((i * Element * Correlation * Eta - B1)^2 - (Eta)^2 * ((2 * i * Element * U1) - (Vols_L)^2));
d2= sqrt((i * Element * Correlation * Eta - B2)^2 - (Eta)^2 * ((2 * i * Element * U2) - (Vols_L)^2));
 
G1= (B1 - (i * Element * Correlation * Eta) + d1) / (B1 - (i * Element * Correlation * Eta) - d1);
G2= (B2 - (i * Element * Correlation * Eta) + d2) / (B2 - (i * Element * Correlation * Eta) - d2);
 
D1= ((B1 - (i * Element * Correlation * Eta) + d1)/ (Eta)^2) * ((1 - exp(d1 * Calendar_L)) / (1 - (G1 * exp(d1 * Calendar_L))));
D2= ((B2 - (i * Element * Correlation * Eta) + d2)/ (Eta)^2) * ((1 - exp(d2 * Calendar_L)) / (1 - (G2 * exp(d2 * Calendar_L))));
 
C1= (i * Element * (R_L - Q_L) * Calendar_L) + (A/(Eta)^2) * ((B1 - ((i * Element * Correlation * Eta) + d1) * Calendar_L) - 2 * log((1 - (G1 * exp(d1 * Calendar_L))) / (1 - G1)));
C2= (i * Element * (R_L - Q_L) * Calendar_L) + (A/(Eta)^2) * ((B2 - ((i * Element * Correlation * Eta) + d1) * Calendar_L) - 2 * log((1 - (G2 * exp(d1 * Calendar_L))) / (1 - G2)));
 
F1= exp(C1 + (D1 * (Vols_L)^2) + ((i * Vols_L) * Spot));
F2= exp(C2 + (D2 * (Vols_L)^2) + ((i * Vols_L) * Spot));
 
% ~ PDE's ~ 
 
int1= (exp(-i * Element * log(Strikes_L)) * F1) / (i * Element); % Function I
int2= (exp(-i * Element * log(Strikes_L)) * F2) / (i * Element); % Function II
 
int1= real(integral(int1, Element, inf)); % Real part of the Integral Solution
int2= real(integral(int2, Element, inf)); % Real part of the Integral Solution
 
Func1= (1/2) + (1/pi) * int1 * d1 * Element;
Func2= (1/2) + (1/pi) * int2 * d2 * Element;
 
Heston_Price= (Spot_L * Func1) - (Strike_L * exp((- R_L - Q_L) * Calendar_L) * Func2);

Thanks, Cheers.

[John D'Errico]

Because not all integrals that you can pose have an analytical solution? Or perhaps I should write that differently. MOST arbitrary integrals that you might decide to pose lack an analytical solution.

[Walter Roberson]

Is Strike_L the same as Strikes_L ?