integral

Tabla de integrales
∫ dx = x + C
x2
+C
2
∫ xdx =
x n +1
∫ x dx = n + 1 + C , (n ≠ −1)
n
1
∫ x dx = ln x + C
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∫ kdx = kx + C
x3
+C
3
2
∫ x dx =
n
∫ u ' u dx =
u'
∫u
u n +1
+ C , (n ≠ −1)
n +1
dx = ln u + C
∫ x + a dx = ln x + a + C
1
∫ u + a dx = ln u + a + C
∫e
dx = e x + C
∫ u' e
x
ax
+ C , ( a > 0, a ≠ 1)
ln a
x
∫ a dx =
∫ sen xdx = − cos x + C
∫ cos xdx = sen x + C
1
∫ cos
2
dx = tan x + C
x
∫ (1 + tan
1
∫ sen
∫
2
x
1− x
1
2
2
x ) dx = tan x + C
dx = − cotan x + C
1
∫1+ x
∫a
2
2
dx = arcsen x + C
dx = arctan x + C
1
1
x
dx = arctan + C
2
a
a
+x
u'
u
dx = e u + C
au
∫ u ' a dx = ln a + C , (a > 0, a ≠ 1)
u
∫ u' sen udx = − cos u + C
∫ u' cos udx = sen u + C
u'
∫ cos
2
u
dx = tan u + C
∫ u ' (1 + tan
2
u ) dx = tan u + C
u'
∫ sen u dx = −cotan u + C
2
u'
∫
1− u2
u'
∫1+ u
∫a
2
2
dx = arcsen u + C
dx = arctan u + C
u'
1
u
dx = arctan + C
2
+u
a
a
Integral de la suma o resta
∫ (u ± v)dx = ∫ udx ± ∫ vdx
Integración por partes
∫ udv = uv − ∫ vdu
Regla de Barrow
∫
Siendo: u, v funciones de x;
b
a
b
f ( x) dx = F ( x) a = F (b) − F (a )
a, k, n, C constantes.