原始関数の一覧
∫ 1 x 2 + α 2 d x = 1 α arctan  x α + C {\displaystyle \int {\frac {1}{x^{2}+\alpha ^{2}}}\,dx={\frac {1}{\alpha }}\arctan {\frac {x}{\alpha }}+C}
∫ 1 ± x 2 ∓ α 2 d x = 1 2 α ln  ( x ∓ α ± x + α ) + C {\displaystyle \int {\frac {1}{\pm x^{2}\mp \alpha ^{2}}}\,dx={\frac {1}{2\alpha }}\ln \left({\dfrac {x\mp \alpha }{\pm x+\alpha }}\right)+C}