原始関数の一覧
∫ a 2 + x 2 x d x = a 2 + x 2 − a ln  ( a + a 2 + x 2 x ) + C {\displaystyle \int {\frac {\sqrt {a^{2}+x^{2}}}{x}}\,dx={\sqrt {a^{2}+x^{2}}}-a\ln \left({\frac {a+{\sqrt {a^{2}+x^{2}}}}{x}}\right)+C}
∫ a 2 + x 2 x 2 d x = ln  ( x + a 2 + x 2 ) − a 2 + x 2 x + C {\displaystyle \int {\frac {\sqrt {a^{2}+x^{2}}}{x^{2}}}\,dx=\ln \left(x+{\sqrt {a^{2}+x^{2}}}\right)-{\frac {\sqrt {a^{2}+x^{2}}}{x}}+C}
∫ 1 a 2 + x 2 d x = ln  ( x + a 2 + x 2 ) + C {\displaystyle \int {\frac {1}{\sqrt {a^{2}+x^{2}}}}\,dx=\ln \left(x+{\sqrt {a^{2}+x^{2}}}\right)+C}
∫ x 2 a 2 + x 2 d x = 1 2 x a 2 + x 2 − 1 2 a 2 ln  ( a 2 + x 2 + x ) + C {\displaystyle \int {\frac {x^{2}}{\sqrt {a^{2}+x^{2}}}}\,dx={\frac {1}{2}}x{\sqrt {a^{2}+x^{2}}}-{\frac {1}{2}}a^{2}\ln \left({\sqrt {a^{2}+x^{2}}}+x\right)+C}
∫ 1 x a 2 + x 2 d x = 1 a ln  ( x a + a 2 + x 2 ) + C {\displaystyle \int {\frac {1}{x{\sqrt {a^{2}+x^{2}}}}}\,dx={\frac {1}{a}}\ln \left({\frac {x}{a+{\sqrt {a^{2}+x^{2}}}}}\right)+C}
∫ 1 x 2 a 2 + x 2 d x = − a 2 + x 2 a 2 x + C {\displaystyle \int {\frac {1}{x^{2}{\sqrt {a^{2}+x^{2}}}}}\,dx=-{\frac {\sqrt {a^{2}+x^{2}}}{a^{2}x}}+C}
本項は、原始関数の一覧(げんしかんすうのいちらん)である。以下、積分定数は C {\displaystyle C} とする。