During my attempt to solve the non-linear ODE
\begin{equation} m\ddot{x}+x-x^3=0 \end{equation} I have stumbled across the integral: \begin{equation} \int{\frac{1}{\sqrt{\frac{1}{m}\left( \frac{x^4}{2}-x^2\right)+2c}}dx} \end{equation} which is blocking my way to solution. Now, I have some experience with these integrals, but apparently not enough, to know that I will probably use a hyperbolic trigonometric substitution in order to reach the solution.
So, what should I do?
Thanks!