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Dit artikel bevat een lijst van integralen van inverse hyperbolische functies .
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r
s
i
n
h
x
a
d
x
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x
a
r
s
i
n
h
x
a
−
x
2
+
a
2
+
C
{\displaystyle \int \mathrm {arsinh} \,{\frac {x}{a}}\,dx=x\,\mathrm {arsinh} \,{\frac {x}{a}}-{\sqrt {x^{2}+a^{2}}}+C}
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a
r
c
o
s
h
x
a
d
x
=
x
a
r
c
o
s
h
x
a
−
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}
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a
r
t
a
n
h
x
a
d
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a
r
t
a
n
h
x
a
+
a
2
ln
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a
2
−
x
2
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+
C
(voor
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x
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<
|
a
|
)
{\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{)}}}
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a
r
c
o
t
h
x
a
d
x
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a
r
c
o
t
h
x
a
+
a
2
ln
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x
2
−
a
2
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+
C
(voor
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x
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>
|
a
|
)
{\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{)}}}
∫
a
r
s
e
c
h
x
a
d
x
=
x
a
r
s
e
c
h
x
a
−
a
a
r
c
t
a
n
x
a
−
x
a
+
x
x
−
a
+
C
(voor
x
∈
(
0
,
a
)
)
{\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{)}}}
∫
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r
c
s
c
h
x
a
d
x
=
x
a
r
c
s
c
h
x
a
+
a
ln
x
+
x
2
+
a
2
a
+
C
(voor
x
∈
(
0
,
a
)
)
{\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{)}}}
