Home
Random
Log in
Settings
Donate
About Wikiversity
Disclaimers
Search
Tích phân hàm số toán nghịch
Language
Watch
Edit
∫
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
|
(
|
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{( }}|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
|
(
|
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{( }}|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
(
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{( }}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
(
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{( }}x\in (0,\,c){\mbox{)}}}
