Q on 10.8#2

Hello, Dr. Taylor.

I am not sure what integration technique I can use to integrate the magnitude of r'(t). 
Should I be approaching this problem
differently?

Thanks.

******************

Well, r'(t)=<10√2, 10e^(10t), -10e^(-10t)>, so

thus

at which point you can look up the answer in your table of integrals.
Remark: I bet someone thought that you would never need to know hyperbolic trig functions