Hi. I've been struggling with this for hours and not getting anywhere even after a hint from a teacher. I have to integrate (indefinite integral) v / (1+cv²) where c is a constant. The hint the teacher gave was that the integral of 1 / (1+v²) is tan^-1(v), but I can't see how to use this unless I use integration by parts - which yields another term which involves integrating tan^-1, which we haven't been taught so I assume I'm not expected to do and thus I'm doing something wrong. I also attempted to do it by the "if the derivative of the bottom is the top then the solution is ln |bottom|, giving the solution 1/c ln |1+v²|. The problem with this is that I then have to input v=dy/dx , rearrange and solve again to get the form I need (it's part of a question on solving a nonlinear autonomous ordinary differential equation) which, when I tried, was insanely complicated - well beyond the level I'm supposed to be working at. I'm completely stumped so can anyone be of assistance here? I can describe the full problem if there's not enough information here on the nature of the problem.