Taula integrals - fev PDF

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Tabla de integrales

∫ dx = x + C

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∫ kdx = kx + C x3 +C 3

∫ xdx =

x2 +C 2

2 ∫ x dx =

n ∫ x dx =

x n +1 + C , (n ≠ −1) n +1

n ∫ u' u dx =

1

∫x

1

∫ x + a dx = ln x + a ∫e

x

+C

dx = e x + C

x ∫ a dx =

u' dx = ln u + C u

∫

dx = ln x + C

ax + C , (a > 0, a ≠ 1) ln a

u n+ 1 + C , (n ≠ −1) n+1

u'

∫ u + a dx = ln u + a + C ∫ u'e

u

dx = e u + C

u ∫ u ' a dx =

au + C, ( a > 0, a ≠ 1) ln a

∫ sen xdx = − cos x + C

∫ u ' senudx = − cosu + C

∫ cos xdx = sen x + C

∫ u ' cosudx = sen u + C

1

∫ cos

2

dx = tan x + C

x

∫ (1 + tan 1

∫ sen ∫

2

x

1− x

1

∫a

2

2

x) dx = tan x + C

dx = − cotan x + C

1

∫1 + x

2

2

dx = arcsen x + C

dx = arctan x + C

1 1 x dx = arctan + C a a + x2

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' u 1 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....