Document

Tabla de integrales
∫
dx
∫x
2
∫ sen udu
∫
a u du
∫
∫
∫ sec
b
⌠
⌡
2
udu
dudx
f(x)
∫aa
2
−u2
u
e du
∫
∫ thxdx
Cálculo Integral para primeros cursos universitarios. Alejandre - Allueva, http://ocw.unizar.es
TABLA DE INTEGRALES
1)
∫ dx [ f ( x )] dx = f(x) + C
2)
∫ [ f (x ) ± g (x )] dx = ∫ f ( x ) dx ± ∫ g ( x ) dx
3)
∫ k f ( x ) dx = k ∫ f ( x ) dx
d
f ′( x ) f (x ) m dx =
[ f ( x )] m+1
4)
∫
5)
∫ f ( x ) dx = Log f ( x )
f ′( x )
f ′( x ) a f (x )dx =
m +1
k = cte.
+C
+C
a f (x)
+C
Loga
6)
∫
7)
∫ f ′( x ) e
8)
∫ f ′( x ) sen [ f (x )] dx = − cos[ f ( x )] + C
9)
∫ f ′( x ) cos[ f (x )] dx = sen [ f ( x )] + C
f (x)
m =/ −1
dx = e f (x ) + C
Cálculo Integral para primeros cursos universitarios. Alejandre - Allueva, http://ocw.unizar.es
Tabla de integrales
227
10)
∫ f ′( x ) tg [ f (x )] dx = − Log cos [ f ( x )]
+C
11)
∫ f ′( x ) cotg[ f (x )] dx = Log sen [ f ( x )]
+C
12)
∫ f ′( x ) sec[ f ( x )] dx = Log sec [ f ( x )] + tg[ f ( x )]
13)
∫ f ′( x ) cosec[ f ( x )] dx = Log cosec[ f ( x )] − cotg [ f ( x )]
14)
∫ f ′( x ) sec [ f ( x )] dx = tg[ f ( x )] + C
15)
∫ f ′( x ) cosec [ f ( x )] dx = − cotg [ f ( x )] + C
16)
∫ f ′( x ) sec [ f ( x )] tg [ f (x )] dx = sec[ f (x )] + C
17)
∫ f ′( x ) cosec[ f ( x )] cotg[ f ( x )] dx = − cosec[ f (x )] + C
18)
∫
+C
+C
2
2
f ′( x )
a 2 − [ f (x )]
2
f (x) 
dx = arcsen 
 +C
 a 
Cálculo Integral para primeros cursos universitarios. Alejandre - Allueva, http://ocw.unizar.es
228
Introducción al cálculo integral
− f ′( x )
19)
∫
20)
∫ a + [ f ( x )]
a 2 − [ f (x )]2
f ′( x )
2
2
f ′( x )
f (x) 
dx = arccos 
 +C
 a 
1
f (x) 
dx = arctg 
 +C
a
 a 
[ f ( x )] 1− n
21)
∫ [ f ( x )]
22)
∫ 1 − [ f ( x )]
23)
∫ [ f ( x )]
24)
∫ [ f ( x )]
25)
∫ f ′( x ) sh [ f (x )] dx = ch[ f ( x )] + C
26)
∫ f ′( x ) ch [ f ( x )] dx = sh [ f ( x )] + C
27)
∫ f ′( x ) th [ f (x )] dx = Log ch[ f (x )] + C
dx =
n
f ′( x )
2
+1
f ′( x )
2
−1
n ≠1
+C
dx = argth [ f ( x )] + C =
f ′( x )
2
1− n
1
| 1+ x |
Log
+C
2
| 1− x |
dx = argsh [ f ( x )] + C= Log x + x 2 + 1 + C
dx = argch [ f ( x )] + C = Log x + x 2 − 1 + C
Cálculo Integral para primeros cursos universitarios. Alejandre - Allueva, http://ocw.unizar.es
Tabla de integrales
229
f ′( x )
28)
∫ ch [ f ( x )] dx = th [ f ( x )] + C
29)
∫ f ′( x ) sech[ f ( x )] dx = 2arctg e
30)
∫ f ′( x ) cosech[ f (x )] dx = Log th [ f ( x ) 2]
31)
∫ f ′( x )argsh 
32)
∫ f ′( x )argch 
33)
∫ f ′( x )argth 
2
f (x )
+C
+C
 f ( x ) dx = f (x )argsh  f ( x )  −



a 
 a 
[ f ( x )]2 + a 2
+C
 f ( x ) dx = f (x )argch  f (x )  ± [ f ( x )]2 − a 2 + C



a 
 a 


 f (x) 
 f (x ) 
 − si argch 
 > 0; + si argch 
 < 0 
 a 
 a 


 f (x )  dx = f (x )argth  f (x )  +



a 
 a 
a
+ Log f 2 ( x ) − a 2 + C
2
Cálculo Integral para primeros cursos universitarios. Alejandre - Allueva, http://ocw.unizar.es