Indefinite integral including cos

Question

Does anyone have a solution to the following indefinite integral?

$$ F(x)=\frac{1}{4} \int (1-[1-\cos\phi_1-\cos\phi_2]^2) \, dx $$ where $$ \tan\phi_1=\frac{k_1}{x} \ , \ \tan\phi_2=\frac{k_2}{k_3-x} $$

Answer 1

Hint: Note that since tan = opp/adj, it follows that if $\tan\theta =A/B$, then $\sin\theta=\frac{\pm A}{\sqrt{A^2+B^2}}$ and $\cos\theta =\frac{\pm B}{\sqrt{A^2+B^2}}$. The signs $\pm$ are the same but ambiguous because $\frac{A}{B}=\frac{-A}{-B}$.