∫ dx/x^2+x-1
[m] ∫ _{2}^{+ ∞ }\frac{dx}{x^2+x-1}=lim_{A →+ ∞ } ∫ _{2}^{A}\frac{dx}{(x+\frac{1}{2})^2-\frac{5}{4}}=[/m]
Табличный интеграл [r] [m] ∫ \frac{dx}{x^2-a^2}=\frac{1}{2a}ln|\frac{x-a}{x+a}|+C[/m][/r]
[m]=lim_{A →+ ∞ }\frac{1}{2\cdot \frac{\sqrt{5}}{2}}ln|\frac{x+\frac{1}{2}-\frac{\sqrt{5}}{2}}{x+\frac{1}{2}+\frac{\sqrt{5}}{2}}|)| _{2}^{A}=\frac{1}{\sqrt{5}}lim_{A →+ ∞ }(ln|\frac{2x+1-\sqrt{5}}{2x+1+\sqrt{5}}|)| _{2}^{A}=\frac{1}{\sqrt{5}}ln1-\frac{1}{\sqrt{5}}(ln|\frac{2\cdot 2+1-\sqrt{5}}{2\cdot +1+\sqrt{5}}|)[/m]