原始関数の一覧
∫ x a + b x d x = 2 15 b 2 ( 3 b x − 2 a ) ( a + b x ) 3 2 + C {\displaystyle \int x{\sqrt {a+bx}}\,dx={\frac {2}{15b^{2}}}(3bx-2a)(a+bx)^{\frac {3}{2}}+C}
∫ x 2 a + b x d x = 2 105 b 3 ( 15 b 2 x 2 − 12 a b x + 8 a 2 ) ( a + b x ) 3 2 + C {\displaystyle \int x^{2}{\sqrt {a+bx}}\,dx={\frac {2}{105b^{3}}}(15b^{2}x^{2}-12abx+8a^{2})(a+bx)^{\frac {3}{2}}+C}
∫ x n a + b x d x = 2 b ( 2 n + 3 ) x n ( a + b x ) 3 2 − 2 n a b ( 2 n + 3 ) ∫ x n − 1 a + b x d x {\displaystyle \int x^{n}{\sqrt {a+bx}}\,dx={\frac {2}{b(2n+3)}}x^{n}(a+bx)^{\frac {3}{2}}-{\frac {2na}{b(2n+3)}}\int x^{n-1}{\sqrt {a+bx}}dx}