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

LibnizBest ResponseYou've already chosen the best response.0
show the work; I am not interested in solution
 one year ago

Jemurray3Best ResponseYou've already chosen the best response.1
\[ \large \int_{\infty}^\infty e^{x^2} e^{xy} dx = \int e^{(x^2+xy)}dx = e^{y^2/4}\int e^{(x^2+xy+y^2/4)}dx\] \[ \large = e^{y^2/4}\int e^{(x+y/2)^2}dx = \sqrt{\pi}\cdot e^{y^2 / 4}\]
 one year ago

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

Jemurray3Best ResponseYou've already chosen the best response.1
I didn't. I multiplied the integrand by exp(y^2/4) and to compensate multiplied the outside by exp(y^2/4).
 one year ago
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