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
2026-03-26 11:06:16.1774523176
Integrating shifted Gaussian and a polynomial function
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