有理関数の原始関数の一覧
∫ 1 ( a x 2 + b x + c ) n d x = 2 a x + b ( n − 1 ) ( 4 a c − b 2 ) ( a x 2 + b x + c ) n − 1 + ( 2 n − 3 ) 2 a ( n − 1 ) ( 4 a c − b 2 ) ∫ 1 ( a x 2 + b x + c ) n − 1 d x + C {\displaystyle \int {\frac {1}{(ax^{2}+bx+c)^{n}}}dx={\frac {2ax+b}{(n-1)(4ac-b^{2})(ax^{2}+bx+c)^{n-1}}}+{\frac {(2n-3)2a}{(n-1)(4ac-b^{2})}}\int {\frac {1}{(ax^{2}+bx+c)^{n-1}}}dx+C}