逆三角関数の原始関数の一覧
∫ arcsec  x d x = x arcsec  x − arctanh 1 − 1 x 2 + C {\displaystyle \int \operatorname {arcsec} x\,dx=x\operatorname {arcsec} x-\operatorname {arctanh} \,{\sqrt {1-{\frac {1}{x^{2}}}}}+C}
∫ arcsec  a x d x = x arcsec  a x − 1 a arctanh 1 − 1 a 2 x 2 + C {\displaystyle \int \operatorname {arcsec} ax\,dx=x\operatorname {arcsec} ax-{\frac {1}{a}}\,\operatorname {arctanh} \,{\sqrt {1-{\frac {1}{a^{2}x^{2}}}}}+C}
∫ x arcsec  a x d x = x 2 arcsec  a x 2 − x 2 a 1 − 1 a 2 x 2 + C {\displaystyle \int x\operatorname {arcsec} ax\,dx={\frac {x^{2}\operatorname {arcsec} ax}{2}}-{\frac {x}{2\,a}}{\sqrt {1-{\frac {1}{a^{2}x^{2}}}}}+C}