Ok, it's not 24.9. It's 20. Very nice expression you have there.
sec^2 integral is easy, giving root3, so +3-1 at the end of the expression.
The other integral comes out as tan^-1(e^x) between r and 0. tan^-1 in this sense is the inverse of tan, not cot.
As x -> infinity, e^x -> infinity...