Spisak integrala inverznih hiperboličkih funkcija
Slijedi spisak integrala (antiderivacija funkcija) inverznih (arc) hiperboličkih funkcija. Za potpuni spisak integrala funkcija, pogledajte tabela integrala i spisak integrala. ∫ a r s i n h x c d x = x a r s i n h x c − x 2 + c 2 {\displaystyle \int \mathrm {arsinh} \,{\frac {x}{c}}\,dx=x\,\mathrm {arsinh} \,{\frac {x}{c}}-{\sqrt {x^{2}+c^{2}}}} ∫ a r c o s h x c d x = x a r c o s h x c − x 2 − c 2 {\displaystyle \int \mathrm {arcosh} \,{\frac {x}{c}}\,dx=x\,\mathrm {arcosh} \,{\frac {x}{c}}-{\sqrt {x^{2}-c^{2}}}} ∫ a r t a n h x c d x = x a r t a n h x c + c 2 ln ⁡ | c 2 − x 2 | (for  | x | < | c | ) {\displaystyle \int \mathrm {artanh} \,{\frac {x}{c}}\,dx=x\,\mathrm {artanh} \,{\frac {x}{c}}+{\frac {c}{2}}\ln |c^{2}-x^{2}|\qquad {\mbox{(for }}|x|<|c|{\mbox{)}}} ∫ a r c o t h x c d x = x a r c o t h x c + c 2 ln ⁡ | x 2 − c 2 | (for  | x | > | c | ) {\displaystyle \int \mathrm {arcoth} \,{\frac {x}{c}}\,dx=x\,\mathrm {arcoth} \,{\frac {x}{c}}+{\frac {c}{2}}\ln |x^{2}-c^{2}|\qquad {\mbox{(for }}|x|>|c|{\mbox{)}}} ∫ a r s e c h x c d x = x a r s e c h x c − c a r c t a n x c − x c + x x − c (for  x ∈ ( 0 , c ) ) {\displaystyle \int \mathrm {arsech} \,{\frac {x}{c}}\,dx=x\,\mathrm {arsech} \,{\frac {x}{c}}-c\,\mathrm {arctan} \,{\frac {x\,{\sqrt {\frac {c-x}{c+x}}}}{x-c}}\qquad {\mbox{(for }}x\in (0,\,c){\mbox{)}}} ∫ a r c s c h x c d x = x a r c s c h x c + c ln x + x 2 + c 2 c (for  x ∈ ( 0 , c ) ) {\displaystyle \int \mathrm {arcsch} \,{\frac {x}{c}}\,dx=x\,\mathrm {arcsch} \,{\frac {x}{c}}+c\,\ln \,{\frac {x+{\sqrt {x^{2}+c^{2}}}}{c}}\qquad {\mbox{(for }}x\in (0,\,c){\mbox{)}}}