Help in integration in MATLAB?

syms w
L = (5.*(i.*w).^5 - 170.*(i.*w).^3 + 1125.*(i.*w))./(5.*(i.*w).^7 + 7.5.*(i.*w).^6 - 170.*(i.*w).^5 - 255.*(i.*w).^4 + 1125.*(i.*w).^3 + 1688.*(i.*w).^2);
S = 1./(1 + L);

int(log(abs(S)),[0 inf])

I need to integrate the log of the absolute value of S (w being the variable) from 0 to infinity. But MATLAB cannot do it, anyways to approximate this integral in MATLAB or any other approaches?

Answer 1

[Star Strider]

If you want a numeric result, use the vpaintegral function —

syms w
L = (5.*(i.*w).^5 - 170.*(i.*w).^3 + 1125.*(i.*w))./(5.*(i.*w).^7 + 7.5.*(i.*w).^6 - 170.*(i.*w).^5 - 255.*(i.*w).^4 + 1125.*(i.*w).^3 + 1688.*(i.*w).^2);
S = 1./(1 + L);
LaS = simplify(log(abs(S)), 500);

LaS = 

IntLaS = int(LaS,[0 Inf])

IntLaS = 

IntS = vpaintegral(log(abs(S)),[0 inf])

IntS = 

0.0000411287

It probably does not have an analytic (symbolic) solution.

.

[John D'Errico]

Probably? That seems a mild understatement. :)