Question Number 147835 by peter frank last updated on 23/Jul/21
$${prove}\:{that}\: \\ $$$$\:\:\int\mathrm{cos}\:\mathrm{2}\theta{log}\left(\frac{\mathrm{cos}\:\theta+\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta−\mathrm{sin}\:\theta}\right)=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}\theta{log}\left[\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}+\theta\right)+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}\:\left(\mathrm{cos}\:\mathrm{2}\theta\right)\right. \\ $$$$ \\ $$