Solve the integral I=∫R∞GMmx2dx
I=∫R∞GMmx2dx=GMm∫R∞dxx2=GMm[−1x]R∞
=GMm∣∣∣−1R+1∞∣∣∣=−GMmR
This expression represents the gravitational potential energy which is obtained by integrating GMm/x2 between the limits infinity (∞) and radius of the earth (R).