you cannot integrate this, unless you let x go to infinity.
However you can approximate it via it's Taylor Series
It doesn't. Read this: Integration of Nonelementary Functions
If k = 1.24 , then
It will approach very small error.
Could you find k or k(x) to minimum error ?
If we let limit of error to 0, it mean we get formulation
As your claim, "There are two things you should never try to prove ...... the impossible and the obvious."
You never prove it doesn't.