Let $\alpha \in (0,\frac{\pi }{2})$, be constant. If the integral $\int \frac{\mathrm{t}\mathrm{a}\mathrm{n}x+\mathrm{t}\mathrm{a}\mathrm{n}\alpha }{\mathrm{t}\mathrm{a}\mathrm{n}x-\tan \alpha }dx=A\left(x\right)\mathrm{c}\mathrm{o}\mathrm{s}2\alpha +B\left(x\right)\mathrm{s}\mathrm{i}\mathrm{n}2\alpha +C$, where C is a constant of integration, then the functions $A\left(x\right)$ and $B\left(x\right)$ are respectively