\int\frac{dt}{\sqrt{1+t+t^2}}=\\ \int\frac{dt}{\sqrt{(t+\frac{1}{2})^2+\frac{3}{4}}}\stackrel{tabl.int.}{=}\\
 \mathop{Arsh}\frac{t+\frac{1}{2}}{\frac{\sqrt 3}{2}}=\mathop{Arsh}\frac{2t+1}{\sqrt 3}