\int\frac{dx}{\sqrt{e^{2x}+e^{x}+1}}=/t=e^{x}/=\int\frac{dt}{t\sqrt{t^{2}+t+1}}=/u=\frac{1}{t}/=-\int\frac{du}{\sqrt{u^{2}+u+1}}=-ln|u+\frac{1}{2}+\sqrt{u^{2}+u+1}|+C=-ln|e^{-x}+\frac{1}{2}+e^{-x}\sqrt{e^{2x}+e^{x}+1}|+C