How can I get the expected results of 2 from this integral?
Assuming[{U, k} \[Element] Reals && k > 0, (
Integrate[
2 (U Exp[\[ImaginaryJ] k x])^2, {x, -\[Infinity], \[Infinity]}] //
HoldForm)/(
Integrate[(U Exp[\[ImaginaryJ] k x])^2, {x, -\[Infinity], \
\[Infinity]}] // HoldForm) // FullSimplify]
Limit[Integrate[(Exp[\[ImaginaryJ] k x])^2, {x, -a, a}, Assumptions -> a > 0], a -> Infinity]
produces and the same with the denominator. $\endgroup$HoldForm
the integral does not evaluate at all. The issue then is, how to pull2
from withinIntegrate
in the numerator, and then how to convince Mathematica to cancel the two identical expressions. Experienced users of this site know what to do, but it is not surprising that those less experienced do not. By the way, it took me a few minutes to realize thatHoldForm
needed to be replaced byUnevaluated
. $\endgroup$