The strong nuclear force increases with distance,

The strong nuclear force increases with distance, $a(r)=r$. It binds quarks so tightly that up to now no quarks have been seen (reliably). Problem 28 gives $q_{\theta \theta }+q=1/q^3$.
(a) Multiply by $q_{\theta }$ and integrate to find $\frac{1}{2}{q}_{\theta }^2+\frac{1}{2}{q}^2=\text{\_\_\_\_}+C$.
*(b) Integrate again (with tables) after setting $u=q^2$, $u_{\theta }=2q{q}_{\theta }$.

This exercise builds on another exercise in its source book, which isn't shown here.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §12.4 Polar Coordinates and Planetary Motion, #30