Passing NIntegrate through NSolve?

Hello,

I am trying to numerically solve an integral with respect to variable u, pass the solution through an exponential function, and subsequently set that function equal to a particular integer K and numerically solve for u. When I do this, I get a non-numerical answer–or at least an answer that I do not know how to convert to a number. Any suggestions would be greatly appreciated!

Alex

test1.nb (7.08 KB)