Question Number 104927 by bobhans last updated on 24/Jul/20
$$\int\frac{{dx}}{\mathrm{1}+{x}+{x}^{\mathrm{2}} } \\ $$
Answered by Dwaipayan Shikari last updated on 24/Jul/20
$$\int\frac{{dx}}{\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{\mathrm{2}} }=\:\frac{\mathrm{2}}{\:\sqrt{\mathrm{3}}}{tan}^{−\mathrm{1}} \frac{\mathrm{2}{x}+\mathrm{1}}{\:\sqrt{\mathrm{3}}}+{C} \\ $$