aha!

its easier than i thought. make that substitution and you will get an integral you can actually evaluate directly.

we started from

sub

so

To get

you can evaluate that integral using standard methods. hopefully the right answer drops out!

(reminder: and

editi did it to check:

Evaluating the integral gives

Which simplifies to the required answer.

phew!

not bad for an economist, if i do say so myself....even if it took about 10 tries