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Tabla de integrales
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∫ dx = x + C
∫ kdx = kx + C
x2 ∫ xdx = 2 + C
x3 ∫ x dx = 3 + C
x n +1 + C , (n ≠ −1) n +1
n ∫ x dx =
1
∫ x dx = ln x + C
2
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 +x a a
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
f ( x)dx = F ( x) a = F (b) − F (a )
a, k, n, C constantes.
b