Let's consider the uniform convergence of the integral $ \displaystyle \int\limits_0^\infty f(x,y)dx $ on the some segment $[c,d]$. We know the Weierstrass M-test as the sufficient condition of uniform convergence. Is there any simple countexplamle proving that M-test is not neccesary?
I know the example $ \displaystyle\int\limits_1^\infty e^{-\frac{1}{y^2}(x-\frac{1}{y})^2}dx $. Is there any simpler examples?
Thanks for the help!