Exponential function produces error with integrate command

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Ben Miller
Ben Miller 2020-12-7
编辑： Ben Miller 2020-12-7
Hello. I'm relatively new to Matlab, and I have the following problem which boils down from a larger, more complicated integral, but for now I am working with a simplified case. I believe that I have found the source of my problem.
I wrote
fun = @(x) (exp(x).*exp(-(x.^2)/2);
q = integral(fun,-1,Inf)
The value of q is then NaN.
Why is this the case? I evaluated this integral in Wolfram Alpha and received a number.

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David Goodmanson
David Goodmanson 2020-12-7
编辑：David Goodmanson 2020-12-7
Hi Ben
for large x, exp(x) overflows to infinity before the exp(-(x.^2)/2) factor has a chance to bring in down. Try completing the square in the exponent:
fun = @(x) exp(-((x-1).^2)/2)*exp(1/2)
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Ben Miller
Ben Miller 2020-12-7
编辑：Ben Miller 2020-12-7
That is what I suspected, and if I combine everything into one exp expression it works.

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