the given vector and the bounds of integration are;

differentiation gives;

definition of the length of a curve (were refers to the magnitude of the vector );

substituting the magnitude of and the bounds of integration into the equation;

So every problem, of this general form, so far has had a very simple integration where there is ultimately just a constant under the radical. So I think I'm looking for a way to combine the exponential functions into a constant and I can't come up with it so far.

If this is the wrong strategy please let me know.