Find the arc length of the givenn curve on the given innterval

x=e^-tcost, y=e^-tsint, 0<t<pi/2

so I figured out dx/dt and dy/dt to be -e^-tsint-e^-tcost and e^-tcost-e^-tsint respectively.

And then ... integeral(0to pi/2) of square root of dy/dt^2 + dx/dt^2

However, it gets really mess and when I take the squares of dx/dt and dy/dt it becomes really messy. Is there a better way to work through this problem?