Popis integrala inverznih hiperbolnih funkcija

Slijedi popis integrala (antiderivacija funkcija) inverznih (area) hiperbolnih funkcija. Za potpun popis integrala funkcija, pogledati tablicu integrala i popis integrala.

[math]\displaystyle{ \int\operatorname{Arsh}\frac{x}{c}\,dx = x\,\operatorname{Arsh}\,\frac{x}{c}-\sqrt{x^2+c^2} + C }[/math]

[math]\displaystyle{ \int\operatorname{Arch}\frac{x}{c}\,dx = x\,\operatorname{Arch}\,\frac{x}{c}-\sqrt{x^2-c^2} + C }[/math]

[math]\displaystyle{ \int\operatorname{Arth}\frac{x}{c}\,dx = x\,\operatorname{Arth}\,\frac{x}{c} + \frac{c}{2}\ln|c^2 - x^2| + C \qquad\mbox{(za }|x|\lt |c|\mbox{)} }[/math]

[math]\displaystyle{ \int\operatorname{Arcth}\frac{x}{c}\,dx = x\,\operatorname{Arcth}\,\frac{x}{c} + \frac{c}{2}\ln|x^2 - c^2| + C \qquad\mbox{(za }|x|\gt |c|\mbox{)} }[/math]

[math]\displaystyle{ \int\operatorname{Arsech}\frac{x}{c}\,dx = x\,\operatorname{Arsech}\,\frac{x}{c} - c\,\mathrm{arctan}\,\frac{x\,\sqrt{\frac{c - x}{c + x}}}{x - c} + C \qquad\mbox{(za } x \in (0,\,c) \mbox{)} }[/math]

[math]\displaystyle{ \int\operatorname{Arcosech}\frac{x}{c}\,dx = x\,\operatorname{Arcosech}\,\frac{x}{c} + c\,\ln\,\frac{x + \sqrt{x^2 + c^2}}{c} + C \qquad\mbox{(za } x \in (0,\,c) \mbox{)} }[/math]