Libniz
\[\int_{inf}^{inf} e^{x^2}e^{x y} dx\]



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@myininaya ,@amistre64

gezimbasha
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I think this is the solution\[e^{\frac{y^2}{4}}\sqrt{\pi}\]

Libniz
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show the work; I am not interested in solution

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@zarkon

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@Jemurray3

Jemurray3
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\[ \large \int_{\infty}^\infty e^{x^2} e^{xy} dx = \int e^{(x^2+xy)}dx = e^{y^2/4}\int e^{(x^2+xy+y^2/4)}dx\]
\[ \large = e^{y^2/4}\int e^{(x+y/2)^2}dx = \sqrt{\pi}\cdot e^{y^2 / 4}\]

Libniz
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how did you get \[\int e^{(x^2+xy)}dx = e^{y^2/4}\]
?

Jemurray3
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I didn't. I multiplied the integrand by exp(y^2/4) and to compensate multiplied the outside by exp(y^2/4).

Libniz
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thanks, man

Jemurray3
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Sure