逆三角関数の原始関数の一覧
∫ arccot  x d x = x arccot  x + ln  ( x 2 + 1 ) 2 + C {\displaystyle \int \operatorname {arccot} x\,dx=x\operatorname {arccot} x+{\frac {\ln \left(x^{2}+1\right)}{2}}+C}
∫ arccot  a x d x = x arccot  a x + ln  ( a 2 x 2 + 1 ) 2 a + C {\displaystyle \int \operatorname {arccot} ax\,dx=x\operatorname {arccot} ax+{\frac {\ln \left(a^{2}x^{2}+1\right)}{2\,a}}+C}
∫ x arccot  a x d x = x 2 arccot  a x 2 + arccot  a x 2 a 2 + x 2 a + C {\displaystyle \int x\operatorname {arccot} ax\,dx={\frac {x^{2}\operatorname {arccot} ax}{2}}+{\frac {\operatorname {arccot} ax}{2\,a^{2}}}+{\frac {x}{2\,a}}+C}