Integral.pdf

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.