逆三角関数の原始関数の一覧
∫ x 2 arccot  a x d x = x 3 arccot  a x 3 − ln  ( a 2 x 2 + 1 ) 6 a 3 + x 2 6 a + C {\displaystyle \int x^{2}\operatorname {arccot} ax\,dx={\frac {x^{3}\operatorname {arccot} ax}{3}}-{\frac {\ln \left(a^{2}x^{2}+1\right)}{6\,a^{3}}}+{\frac {x^{2}}{6\,a}}+C}
∫ x m arccot  a x d x = x m + 1 arccot  a x m + 1 + a m + 1 ∫ x m + 1 a 2 x 2 + 1 d x ( m ≠ − 1 ) {\displaystyle \int x^{m}\operatorname {arccot} ax\,dx={\frac {x^{m+1}\operatorname {arccot} ax}{m+1}}+{\frac {a}{m+1}}\int {\frac {x^{m+1}}{a^{2}x^{2}+1}}\,dx\quad (m\neq -1)}