Help in integration in MATLAB?

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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?

Accepted Answer

Star Strider
Star Strider on 26 Oct 2023
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.
.
  1 Comment
John D'Errico
John D'Errico on 26 Oct 2023
Probably? That seems a mild understatement. :)

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