Anexo:Integrales de funciones inversas hiperbólicas

La siguiente es una lista de integrales de las inversas de las funciones hiperbólicas:

$\int \operatorname {arsinh} {\frac {x}{c}}\,dx=x\operatorname {arsinh} {\frac {x}{c}}-{\sqrt {x^{2}+c^{2}}}$

$\int \operatorname {arcosh} {\frac {x}{c}}\,dx=x\operatorname {arcosh} {\frac {x}{c}}-{\sqrt {x^{2}-c^{2}}}$

$\int \operatorname {artanh} {\frac {x}{c}}\,dx=x\operatorname {artanh} {\frac {x}{c}}+{\frac {c}{2}}\ln \left|c^{2}-x^{2}\right|\qquad ({\text{para }}|x|<|c|)$

$\int \operatorname {arcoth} {\frac {x}{c}}\,dx=x\operatorname {arcoth} {\frac {x}{c}}+{\frac {c}{2}}\ln \left|x^{2}-c^{2}\right|\qquad ({\text{para }}|x|>|c|)$

$\int \operatorname {arsech} {\frac {x}{c}}\,dx=x\operatorname {arsech} {\frac {x}{c}}-c\operatorname {arctan} {\frac {x\,{\sqrt {\frac {c-x}{c+x}}}}{x-c}}\qquad \left({\text{para }}x\in (0,c)\right)$

$\int \operatorname {arcsch} {\frac {x}{c}}\,dx=x\operatorname {arcsch} {\frac {x}{c}}+c\,\ln \,{\frac {x+{\sqrt {x^{2}+c^{2}}}}{c}}\qquad \left({\text{para }}x\in (0,c)\right)$