Lijst van integralen van inverse hyperbolische functies

Dit artikel bevat een lijst van integralen van inverse hyperbolische functies.

${\displaystyle \int \mathrm {arsinh} \,{\frac {x}{a}}\,dx=x\,\mathrm {arsinh} \,{\frac {x}{a}}-{\sqrt {x^{2}+a^{2}}}+C}$

${\displaystyle \int \mathrm {arcosh} \,{\frac {x}{a}}\,dx=x\,\mathrm {arcosh} \,{\frac {x}{a}}-{\sqrt {x^{2}-a^{2}}}+C}$

${\displaystyle \int \mathrm {artanh} \,{\frac {x}{a}}\,dx=x\,\mathrm {artanh} \,{\frac {x}{a}}+{\frac {a}{2}}\ln |a^{2}-x^{2}|+C\qquad {\mbox{(voor }}|x|<|a|{\mbox{)}}}$

${\displaystyle \int \mathrm {arcoth} \,{\frac {x}{a}}\,dx=x\,\mathrm {arcoth} \,{\frac {x}{a}}+{\frac {a}{2}}\ln |x^{2}-a^{2}|+C\qquad {\mbox{(voor }}|x|>|a|{\mbox{)}}}$

${\displaystyle \int \mathrm {arsech} \,{\frac {x}{a}}\,dx=x\,\mathrm {arsech} \,{\frac {x}{a}}-a\,\mathrm {arctan} \,{\frac {x\,{\sqrt {\frac {a-x}{a+x}}}}{x-a}}+C\qquad {\mbox{(voor }}x\in (0,\,a){\mbox{)}}}$

${\displaystyle \int \mathrm {arcsch} \,{\frac {x}{a}}\,dx=x\,\mathrm {arcsch} \,{\frac {x}{a}}+a\,\ln \,{\frac {x+{\sqrt {x^{2}+a^{2}}}}{a}}+C\qquad {\mbox{(voor }}x\in (0,\,a){\mbox{)}}}$