Question Number 174965 by cortano1 last updated on 15/Aug/22
$$\:\:\:\:\:\:\int\:\frac{{x}+\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$
Answered by som(math1967) last updated on 15/Aug/22
$$\int\frac{{x}}{\mathrm{2}{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{dx}+\int\frac{\mathrm{2}{sin}\frac{{x}}{\mathrm{2}}{cos}\frac{{x}}{\mathrm{2}}}{\mathrm{2}{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{dx} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\int{xsec}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}{dx}\:+\int{tan}\frac{{x}}{\mathrm{2}}{dx} \\ $$$$\frac{{x}}{\mathrm{2}}\int{sec}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}{dx}−\frac{\mathrm{1}}{\mathrm{2}}\int\left\{\frac{{dx}}{{dx}}\int{sec}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}{dx}\right\}{dx}+\int{tan}\frac{{x}}{\mathrm{2}}{dx}\: \\ $$$${xtan}\frac{{x}}{\mathrm{2}}\:+{C} \\ $$