What I am trying to solve is $\int_{c}^{\infty} e^{-a(x-b)^2} \frac{(b-c)^2}{x^2 + (b-c)^2} dx$ ,all the constants a,b,c are real and positive. x is also real. I have tried many approaches, like change of variables, integration by parts, Feynman’s Integral Trick but none proved fruitful. I used MATLAB but it also was not able to solve it. I plotted the function of some real and positive values of constants and the function turned out to Gaussian type with finite area. Can anyone help me please?. In dire need of a solution or hint how to solve it
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$\begingroup$ The fact that you integrate from $c$ to $+\infty$, and not from $-\infty$ to $+\infty$ gives few hope for a closed form formula in terms of usual functions. Look for numerical solutions for given values of your parameters $a,b,c$ using the powerful function "integral" of Matlab. $\endgroup$– Jean MarieCommented Apr 6, 2020 at 7:33
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$\begingroup$ Terminology : the second function is not a polynomial but a rational function (quotient of polynomials) having the generic name "Lorentz" or "Cauchy" function. $\endgroup$– Jean MarieCommented Apr 6, 2020 at 7:48
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$\begingroup$ Sorry for the mistake improper naming, Is there any other way than numerical integration, what if a,b,c are generic parameters, what then? $\endgroup$– coolname11Commented Apr 6, 2020 at 8:10
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$\begingroup$ Most integrals haven't a closed form expression... Could you say in which context such an integral is of importance to you ? $\endgroup$– Jean MarieCommented Apr 6, 2020 at 8:22
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$\begingroup$ Ok thanks for all the feedback, I am formulating a problem in communication engineering, and this integral pops out. still thanks $\endgroup$– coolname11Commented Apr 6, 2020 at 8:49
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