reparameterize the curve r(t)=<(e^t)*sin(t), (e^t)*cos(t)> with respect to its arclength measured from (0,1) in the direction of increasing t.
I think that no one has tired answer because of the lack of TeX.
I will try to give some help.
Try to show that ||r’(t)||=e^{t} sqrt(2).
Then s(t)=Integral{0,t} ||r’(u)||du. Write t as function of s; then write r(t(s)).