)
.
why? first do the substitution
and put
then your integral becomes
=\frac{1}{\sqrt{a}} \int_0^{\infty} e^{-x^2} \cos (cx) \ dx.)
differentiating with respect to
(check the conditions that are needed) will give us:
=\frac{1}{\sqrt{a}} \int_0^{\infty} -xe^{-x^2} \sin(cx) \ dx.)
now let
)
and
and apply by parts to get:
=\frac{-c}{2\sqrt{a}} f(c).)
solving this differential equation with the fact that
=\frac{1}{2} \sqrt{\frac{\pi}{a}})
will give us the result.
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Originally Posted by chiph588@ 
