\displaystyle \int_{-m}^{m}\frac{\text{sech}(x\ln{q})}{2\arctan(q^{x})\arctan(q^{-x})+\pi+2}dx=\frac{4}{(\pi+4)\ln{q}}\ln\left(\frac{\arctan(q^{m})+1}{\arctan(q^{-m})+1}\right). 