Integrals containing $ a^2+ u^2$ .

$\displaystyle \int \frac{du}{a^2 + u^2}$ $\displaystyle = \frac 1a \tan^{- 1} \frac ua + C.$ (B..21)
$\displaystyle \int \frac {du}{a^2 - u^2}$ $\displaystyle = \frac {1}{2a} \ln \begin{vmatrix}\frac{u + a}{u - a} \end{vmatrix}+ C.$ (B..22)
$\displaystyle \int \frac {du}{u^2- a^2}$ $\displaystyle = \frac{1}{2a} \ln \begin{vmatrix}\frac{u - a}{u + a} \end{vmatrix}+ C.$ (B..23)



Noah Dana-Picard 2007-12-28