Normalizing a Joint PDF

A certain joint PDF for two random variables XX and YY is given by the following expression:

fXY(x,y)=Cxyey2,f_{XY} (x,y) = Cxy e^{-y^2},

where YY is drawn from (0,)(0,\infty) and XX is drawn from [0,1][0,1].

Find the normalization constant C.C.

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