$\int\limits_{\alpha }^{\beta }$$\frac{dx}{x^{2}+a^{2}}$=$\frac{1}{a}$arctan$\frac{x}{a}$
$\int\limits_{\alpha }^{\beta }$$\frac{dx}{x^{2}-a^{2}}$=$\frac{1}{2a}$$\left| {\frac{x-a}{x+a}} \right|$
$\int\limits_{\alpha }^{\beta }$$\frac{dx}{x^{2}+k}$=ln$\left| {x+\sqrt{x^{2}+k } } \right|$