# Tabla de Integrales

Anuncio
```Tabla de Integrales
Tabla de Primitivas
Departamento de Matem&aacute;ticas
&copy; Ra&uacute;l Gonz&aacute;lez Medina
Formas
Tipos
Simple
Potencial (a  1)
x
a
dx 
1
 x dx
Logar&iacute;tmico
Compuesta
x a 1
a 1
f '&middot;f
f'
 ln x
x
f
x
 e dx  e
x
x
 a dx  a &middot;ln a
Exponencial
 cos xdx
Seno
 senxdx
Coseno
2
x

Arco Seno

1
1x
1
2
2
2
x
a x
f'
 cos (f ) dx
dx  tgx
2
Arco Tangente
a
Neperiano – Arco tangente
2
2
  cosf
 tg (f )
2
2
f'
dx  cotgx
 Sen
x 
x 
  Arc cos  
a
 
a 
1
a f (x )
ln a
 co sec (f )&middot;f 'dx  cotg (f )
 [1  cotg (f )]&middot;f 'dx   cotg (f )
dx  Arcsen 
1 x
&middot;f '(x )dx 
2
dx  Arcsen  x   Arc cos  x 
2
f (x )
2
2
1
a
 sec (f )&middot;f 'dx  tg (f )
 [1  tg (f )]&middot;f 'dx  tg (f )
2
 sen
&middot;f '(x )dx  e f (x )
 senf &middot;f 'dx
 co sec xdx  cotgx
 (1  cotg x )dx  cotgx
Cotangente
dx  ln f
f (x )
  cos x
2
1
f a 1
a 1
 cosf &middot;f 'dx  senf
2
 cos
dx 
e
 senx
 sec xdx  tgx
 (1  tg x )dx  tgx
Tangente
a


f'
1 f 2
f'
2
(f )
dx  cotg (f )
dx  Arcsen f   Arc cos f 
f 
f 
dx  Arcsen    Arc cos  
a
 
a 
a f
2
2
f'
dx  arctg  x 
 1 f
x 
1
1
dx  arctg  
a
x2
a 
a
2
2
dx  arctg f 
f 
f'
1
dx  arctg  
a
f 2
a 
Mx  N
dx  neperiano + arco tangente M  0, ax2  bx  c irreducible
2
 bx  c
 ax
 f (x )  g (x )dx  f (x )dx   g (x )dx
Integral de la suma
 k &middot;f (x )dx
Integral con una cte.
Integraci&oacute;n por simple
Inspecci&oacute;n
r
 g '(x )&middot;[ g (x )] dx

1
[ g (x )]r 1  K
r 1
a
g'(x )
 g (x ) dx  ln g (x )  K
 u &middot;dv  u &middot;v  v &middot;du
Integraci&oacute;n por Partes
Regla de Barrow
 k &middot; f (x )dx
f (x )dx
b
a
 g (a )  g (b )   g (x ) 
b
1
```