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

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gezimbasha
 2 years ago
Best ResponseYou've already chosen the best response.0I think this is the solution\[e^{\frac{y^2}{4}}\sqrt{\pi}\]

Libniz
 2 years ago
Best ResponseYou've already chosen the best response.0show the work; I am not interested in solution

Jemurray3
 2 years ago
Best ResponseYou've already chosen the best response.1\[ \large \int_{\infty}^\infty e^{x^2} e^{xy} dx = \int e^{(x^2+xy)}dx = e^{y^2/4}\int e^{(x^2+xy+y^2/4)}dx\] \[ \large = e^{y^2/4}\int e^{(x+y/2)^2}dx = \sqrt{\pi}\cdot e^{y^2 / 4}\]

Libniz
 2 years ago
Best ResponseYou've already chosen the best response.0how did you get \[\int e^{(x^2+xy)}dx = e^{y^2/4}\] ?

Jemurray3
 2 years ago
Best ResponseYou've already chosen the best response.1I didn't. I multiplied the integrand by exp(y^2/4) and to compensate multiplied the outside by exp(y^2/4).
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