$$\int\_{0}^{c} dy \sqrt{\frac{c-1/2y^2+1/3y^3}{1+2y}}$$ where c is a constant. This is coming from trying to find the area $$\int\_{U \le c} dq\_1dq\_2$$ where $$U=\frac{1}{2}(q\_1^2+q\_2^2)-\frac{1}{3}q\_2^3+q\_1^2q\_2$$ bounded by energy $c=U(q\_1,q\_2)$.