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I'm trying to solve the following:

[tex]f(x) = \int^\infty_{-\infty}ce^{yx-y^2/2} dy[/tex]

where c is a constant

My only idea thus far was that since it is an even function, the expression can be simplified to:

[tex]= 2c\int^\infty_0 e^{y(x-{1/2}y)} dy[/tex]

but I'm stuck here.

Anyone know how to do this?

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# Definite integral: exponential with squared exponent

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