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How does one integrate

[tex]

\int_0^\infty e^{-\beta x^2}\cos{(bx)} dx

[/tex]

for positive beta and real b ?

I was thinking maybe differentiation under the integral sign would do the trick, but I can't get anywhere.

[tex]

\int_0^\infty e^{-\beta x^2}\cos{(bx)} dx

[/tex]

for positive beta and real b ?

I was thinking maybe differentiation under the integral sign would do the trick, but I can't get anywhere.

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