Compute the length of the parametric curve

x=(t2−2)sint+2tcost

y=(2−t2)cost+2tsint

from t1=0 to t2=

I know that I need to square the derivatives, and then add them together, and square root them, and then integrate. Is there anyway to uncomplicate the terms before I start doing the derivative? As it stands, it looks like it will be unnecessarily complicated...