有理関数の原始関数の一覧
∫ 1 x ( a x + b ) d x = − 1 b ln  | a x + b x | + C {\displaystyle \int {\frac {1}{x(ax+b)}}dx=-{\frac {1}{b}}\ln \left|{\frac {ax+b}{x}}\right|+C}
∫ 1 x 2 ( a x + b ) d x = − 1 b x + a b 2 ln  | a x + b x | + C {\displaystyle \int {\frac {1}{x^{2}(ax+b)}}dx=-{\frac {1}{bx}}+{\frac {a}{b^{2}}}\ln \left|{\frac {ax+b}{x}}\right|+C}
∫ 1 x 2 ( a x + b ) 2 d x = − a ( 1 b 2 ( a x + b ) + 1 a b 2 x − 2 b 3 ln  | a x + b x | ) + C {\displaystyle \int {\frac {1}{x^{2}(ax+b)^{2}}}dx=-a\left({\frac {1}{b^{2}(ax+b)}}+{\frac {1}{ab^{2}x}}-{\frac {2}{b^{3}}}\ln \left|{\frac {ax+b}{x}}\right|\right)+C}