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LateToTheParty

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We have a function ψ(x,y,z) = x e

^{[itex]\sqrt{}x2 + y2+ z2[/itex]}

Now I want to integrate this over all space. So I switch to spherical polar include the Jacobian and I end up with a separable integral of sinθ cubed form 0 to pi which is zero. No problem. But here's where the question pops up. I go to calculate the same function except this time with a z in front of the exponential, and I get a different answer, because I no longer get the sin^3 when I switch to spherical. It just seems really odd to me. I apologize if my formatting leaves something to be desired I'm new to the site, and any help would be greatly appreciated. Any insight on why a arbitrary change would affect the behavior of the integral?