Wiki
Support
mar.io
Anexo:Integrales de funciones inversas trigonométricas
La siguiente es una lista de integrales de funciones inversas trigonométricas.
∫
arcsin
x
c
d
x
=
x
arcsin
x
c
+
c
2
−
x
2
{\displaystyle \int \arcsin {\frac {x}{c}}\,dx=x\arcsin {\frac {x}{c}}+{\sqrt {c^{2}-x^{2}}}}
∫
x
arcsin
x
c
d
x
=
(
x
2
2
−
c
2
4
)
arcsin
x
c
+
x
4
c
2
−
x
2
{\displaystyle \int x\arcsin {\frac {x}{c}}\,dx=\left({\frac {x^{2}}{2}}-{\frac {c^{2}}{4}}\right)\arcsin {\frac {x}{c}}+{\frac {x}{4}}{\sqrt {c^{2}-x^{2}}}}
∫
x
2
arcsin
x
c
d
x
=
x
3
3
arcsin
x
c
+
x
2
+
2
c
2
9
c
2
−
x
2
{\displaystyle \int x^{2}\arcsin {\frac {x}{c}}\,dx={\frac {x^{3}}{3}}\arcsin {\frac {x}{c}}+{\frac {x^{2}+2c^{2}}{9}}{\sqrt {c^{2}-x^{2}}}}
∫
arccos
x
c
d
x
=
x
arccos
x
c
−
c
2
−
x
2
{\displaystyle \int \arccos {\frac {x}{c}}\,dx=x\arccos {\frac {x}{c}}-{\sqrt {c^{2}-x^{2}}}}
∫
x
arccos
x
c
d
x
=
(
x
2
2
−
c
2
4
)
arccos
x
c
−
x
4
c
2
−
x
2
{\displaystyle \int x\arccos {\frac {x}{c}}\,dx=\left({\frac {x^{2}}{2}}-{\frac {c^{2}}{4}}\right)\arccos {\frac {x}{c}}-{\frac {x}{4}}{\sqrt {c^{2}-x^{2}}}}
∫
x
2
arccos
x
c
d
x
=
x
3
3
arccos
x
c
−
x
2
+
2
c
2
9
c
2
−
x
2
{\displaystyle \int x^{2}\arccos {\frac {x}{c}}\,dx={\frac {x^{3}}{3}}\arccos {\frac {x}{c}}-{\frac {x^{2}+2c^{2}}{9}}{\sqrt {c^{2}-x^{2}}}}
∫
arctan
x
c
d
x
=
x
arctan
x
c
−
c
2
ln
(
c
2
+
x
2
)
{\displaystyle \int \arctan {\frac {x}{c}}\,dx=x\arctan {\frac {x}{c}}-{\frac {c}{2}}\ln(c^{2}+x^{2})}
∫
x
arctan
x
c
d
x
=
c
2
+
x
2
2
arctan
x
c
−
c
x
2
{\displaystyle \int x\arctan {\frac {x}{c}}\,dx={\frac {c^{2}+x^{2}}{2}}\arctan {\frac {x}{c}}-{\frac {cx}{2}}}
∫
x
2
arctan
x
c
d
x
=
x
3
3
arctan
x
c
−
c
x
2
6
+
c
3
6
ln
c
2
+
x
2
{\displaystyle \int x^{2}\arctan {\frac {x}{c}}\,dx={\frac {x^{3}}{3}}\arctan {\frac {x}{c}}-{\frac {cx^{2}}{6}}+{\frac {c^{3}}{6}}\ln {c^{2}+x^{2}}}
∫
x
n
arctan
x
c
d
x
=
x
n
+
1
n
+
1
arctan
x
c
−
c
n
+
1
∫
x
n
+
1
d
x
c
2
+
x
2
(para
n
≠
−
1
)
{\displaystyle \int x^{n}\arctan {\frac {x}{c}}\,dx={\frac {x^{n+1}}{n+1}}\arctan {\frac {x}{c}}-{\frac {c}{n+1}}\int {\frac {x^{n+1}dx}{c^{2}+x^{2}}}\qquad {\mbox{(para }}n\neq -1{\mbox{)}}}
∫
a
r
c
c
o
t
x
c
d
x
=
x
a
r
c
c
o
t
x
c
+
c
2
ln
(
c
2
+
x
2
)
{\displaystyle \int \mathrm {arccot} \,{\frac {x}{c}}\,dx=x\,\mathrm {arccot} \,{\frac {x}{c}}+{\frac {c}{2}}\ln(c^{2}+x^{2})}
∫
x
a
r
c
c
o
t
x
c
d
x
=
c
2
+
x
2
2
a
r
c
c
o
t
x
c
+
c
x
2
{\displaystyle \int x\,\mathrm {arccot} \,{\frac {x}{c}}\,dx={\frac {c^{2}+x^{2}}{2}}\,\mathrm {arccot} \,{\frac {x}{c}}+{\frac {cx}{2}}}
∫
x
2
a
r
c
c
o
t
x
c
d
x
=
x
3
3
a
r
c
c
o
t
x
c
+
c
x
2
6
−
c
3
6
ln
(
c
2
+
x
2
)
{\displaystyle \int x^{2}\,\mathrm {arccot} \,{\frac {x}{c}}\,dx={\frac {x^{3}}{3}}\,\mathrm {arccot} \,{\frac {x}{c}}+{\frac {cx^{2}}{6}}-{\frac {c^{3}}{6}}\ln(c^{2}+x^{2})}
∫
x
n
a
r
c
c
o
t
x
c
d
x
=
x
n
+
1
n
+
1
a
r
c
c
o
t
x
c
+
c
n
+
1
∫
x
n
+
1
d
x
c
2
+
x
2
(para
n
≠
−
1
)
{\displaystyle \int x^{n}\,\mathrm {arccot} \,{\frac {x}{c}}\,dx={\frac {x^{n+1}}{n+1}}\,\mathrm {arccot} \,{\frac {x}{c}}+{\frac {c}{n+1}}\int {\frac {x^{n+1}dx}{c^{2}+x^{2}}}\qquad {\mbox{(para }}n\neq -1{\mbox{)}}}
ToC
Trending
Día de Acción de Gracias
Manual de supervivencia escolar de Ned
Bárbara Rey
Clasificación de Conmebol para la Copa Mundial de Fútbol de 2026
Luis Caputo
Millonarios Fútbol Club
Al-Nassr Football Club
Nayib Bukele
YouTube
Napoleón Bonaparte
Copa Mundial de Fútbol Sub-17 de 2023
Lionel Messi
Recent Change
Jovan Manev
Maclen
Elección presidencial de México de 2024
We Just Disagree
Paseo de la Virgen
Teatro arena y esteras
Videojuegos para Atari 5200
Khalil Hachimi Idrissi
Clairet Hernández
Clasificación al Campeonato Europeo Sub-17 de la UEFA 2024
Campeonato Europeo Sub-17 de la UEFA 2024
Acción Capital
Medium
|
Medium