I'm trying to prove ; that is, that is Lebesgue integrable over .

Let and .

Since , is an increasing sequence of functions which converges everywhere to .

We want to show that is integrable so it suffices to show converges as . It then follows from the Monotone Convergence Theorem that (and ).

We use the given hint ("don't try to find ; integrate a simpler upper bound instead").

We see that is bounded by. The integral of this upper bound converges, so by comparison test converges.___

My hurdle is filling the gap for an upper bound. is bounded by the constant function 1 but which doesn't converge as . Any suggestions?