1. The problem statement, all variables and given/known data A mass m is thrown vertically from the surface of the earth with a velocity v0. Find a function that describes the velocity v of the mass m in dependance of its distance z from the center of the earth. 2. Relevant equations m*z'' = -G* m*M / z^2 z'' = dv / dt G = gravitational constant M = mass of earth 3. the solution and my problem with it z'' = -G * M * 1/z^2 z'' = dv/dt = v * dv/dz ==> v * dv = -G * M * dz/z^2 Now my Problem: In the next part both sides of the above equation are to be integrated. The left side from v0 to v, and the right side from R to z. Like that: integral(v0..v, v*dv) = -G * M * integral(R..z, dz/z^2) Unfortunately, I dont understand that. Why can I inegrate both sides of the equation like that, and why is it still the same afterwards? What exactly does the term on the left 'integral(v0..v, v*dv)' and the term on the right '-G * M * integral(R..z, dz/z^2)' side of the above equation mean? It would be great if someone could provide a little help!