原始関数の一覧
∫ arccot  x d x = x arccot  x + ln  1 + x 2 + C {\displaystyle \int \operatorname {arccot} x\,dx=x\operatorname {arccot} x+\ln {\sqrt {1+x^{2}}}+C}
∫ arcsec  x d x = x arcsec  x − ln  ( x − x 2 − 1 ) + C {\displaystyle \int \operatorname {arcsec} x\,dx=x\operatorname {arcsec} x-\ln(x-{\sqrt {x^{2}-1}})+C}
∫ arccsc  x d x = x arccsc  x + ln  ( x + x 2 − 1 ) + C {\displaystyle \int \operatorname {arccsc} x\,dx=x\operatorname {arccsc} x+\ln(x+{\sqrt {x^{2}-1}})+C}
∫ 1 a x + b d x = 1 a ln  | a x + b | + C {\displaystyle \int {\frac {1}{ax+b}}\,dx={\frac {1}{a}}\ln \left|ax+b\right|+C}
∫ x a x + b d x = x a − b a 2 ln  | a x + b | + C {\displaystyle \int {\frac {x}{ax+b}}\,dx={\frac {x}{a}}-{\frac {b}{a^{2}}}\ln \left|ax+b\right|+C}
∫ x 2 a x + b d x = 1 2 a 3 ( a 2 x 2 − 2 a b x + 2 b 2 ln  | a x + b | ) + C {\displaystyle \int {\frac {x^{2}}{ax+b}}\,dx={\frac {1}{2a^{3}}}(a^{2}x^{2}-2abx+2b^{2}\ln \left|ax+b\right|)+C}
∫ cot n  x d x = 1 n − 1 cot n − 1  x − ∫ cot n − 2  x d x + C ∀ n ≥ 2 {\displaystyle \int \cot ^{n}x\,dx={\frac {1}{n-1}}\cot ^{n-1}x-\int \cot ^{n-2}x\,dx+C\quad \forall n\geq 2}
∫ cot 2  x d x = − cot  x − x + C {\displaystyle \int \cot ^{2}x\,dx=-\cot x-x+C}
∫ sec n  x d x = 1 n − 1 sec n − 2  x tan  x + n − 2 n − 1 ∫ sec n − 2  x d x + C ∀ n ≥ 2 {\displaystyle \int \sec ^{n}x\,dx={\frac {1}{n-1}}\sec ^{n-2}x\tan x+{\frac {n-2}{n-1}}\int \sec ^{n-2}x\,dx+C\quad \forall n\geq 2}
∫ csc n  x d x = − 1 n − 1 csc n − 2  x cot  x + n − 2 n − 1 ∫ csc n − 2  x d x + C ∀ n ≥ 2 {\displaystyle \int \csc ^{n}x\,dx=-{\frac {1}{n-1}}\csc ^{n-2}x\cot x+{\frac {n-2}{n-1}}\int \csc ^{n-2}x\,dx+C\quad \forall n\geq 2}