1. The problem statement, all variables and given/known data A particle of mass m is subject to a force F(x) = −kx^−2 (1) that attracts it toward the origin. (a) Determine the potential energy function U(x), defined by F(x) = − d U(x)/dx. (b) Assuming that the particle is released from rest at a position x0, show that the time t required for the particle to reach the origin is t = π sqrt(m/8k)(x_0)^(3/2) 2. Relevant equations dt=dx/sqrt(2(E-U)/m) 3. The attempt at a solution So, I found The potential energy to be k/x using that and the fact that at v=0 at x_0, I get dt=dx/sqrt(2((k/x_0)-k/x)/m). My only problem is integrating this I get a long nasty function that I feel I can't get x isolated. Maybe, I'm being lazy and need to gut through it, but is there an easier way to approach this?