How do I solve the integral of the functions x*exp(-a(x-b)^2) and x^2(exp(-a(x-b)^2) where a and b are positive real numbers?(adsbygoogle = window.adsbygoogle || []).push({});

I tried integration by parts and cannot think of how to find the integral. In addition, while I was able to find exp(-a(x-b)^2) in an integral table, the two functions I listed above, I was not able to find. Any hints, suggestions, or integration tables you can point me towards would be appreciated.

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# Two integrals I am trying to solve without closed form antiderivatives

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