I have a 3D particle that is launching with some initial position, velocity, and with a constant force. I can solve for it's position at some time with the following equation:
My goal is to find the distance the particle travels along the trajectory from time 0 to time "t". To solve this, I've tried splitting up the 3D equation into each dimension, taking the magnitude of that addition, and finding the definite integral. Unfortunately, I got stuck at the integration, and Mathematica wasn't giving me an answer. Is this something that can actually be integrated? I've included a snapshot of my Mathematica notebook below. Is my technique wrong?
