An improper integral I = a (x) dx is called absolutely convergent if a |(x)| dx converges. It can be shown

An improper integral I = ∫^∞_a ƒ(x) dx is called absolutely convergent if ∫^∞_a |ƒ(x)| dx converges. It can be shown that if I is absolutely convergent, then it is convergent.

Show that ∫^∞₁ e^−x2 cos x dx is absolutely convergent.