error in integral calculation

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Question:error in integral calculation

Posted: NIMA112 50 Product: Maple 2023

June 06 2025

what is the problem in the integral calculation ?

integral.mw

(1)

G := (ln((1-2*exp(-omega*abs(x-xi))*cos(omega*(y+eta))+exp(-2*omega*abs(x-xi)))/(1-2*exp(-omega*abs(x-xi))*cos(omega*(y-eta))+exp(-2*omega*abs(x-xi))))+ln((1-2*exp(-omega*(x+xi))*cos(omega*(y+eta))+exp(-2*omega*(x+xi)))/(1-2*exp(-omega*(x+xi))*cos(omega*(y-eta))+exp(-2*omega*(x+xi)))))/(4*Pi)

(1/4)*(ln((1-2*exp(-Pi*abs(x-xi)/b)*cos(Pi*(y+eta)/b)+exp(-2*Pi*abs(x-xi)/b))/(1-2*exp(-Pi*abs(x-xi)/b)*cos(Pi*(y-eta)/b)+exp(-2*Pi*abs(x-xi)/b)))+ln((1-2*exp(-Pi*(x+xi)/b)*cos(Pi*(y+eta)/b)+exp(-2*Pi*(x+xi)/b))/(1-2*exp(-Pi*(x+xi)/b)*cos(Pi*(y-eta)/b)+exp(-2*Pi*(x+xi)/b))))/Pi

(2)

int(int(G, xi = 0 .. infinity), eta = 0 .. 1)

Error, (in assuming) when calling 'IntegrationTools:-Indefinite:-Handlers:-LnOnly'. Received: 'invalid input: int/hermiter/horowitzLog expects its 1st argument, f, to be of type ratpoly(anything,x), but received (2*cos(Pi/b*y)*cos(Pi/b*eta)*exp(Pi/b*x)*x1+2*sin(Pi/b*y)*sin(Pi/b*eta)*exp(Pi/b*x)*x1-1)/(1+exp(2*Pi/b*x)*x1^2+(-2*exp(Pi/b*x)*cos(Pi/b*y)*cos(Pi/b*eta)-2*exp(Pi/b*x)*sin(Pi/b*y)*sin(Pi/b*eta))*x1)^2'

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