Tabla de Integrales Inmediatas

Funciones simples
Funciones compuestas
冕dx ⫽ x ⫹ C
INTEGRAL INDEFINIDA
3 TABLA DE INTEGRALES INMEDIATAS
冕kdx ⫽ kx ⫹ C
x
冕x dx ⫽ ᎏ
ᎏ⫹C
n⫹1
冕u
冕 ᎏ1xᎏdx ⫽ ln ⏐x⏐ ⫹ C
'
冕 ᎏuuᎏdx
⫽ ln ⏐u⏐ ⫹ C
冕 e dx ⫽ e ⫹ C
冕 e ⭈ u' ⭈ dx ⫽ e ⫹ C
siendo ⫺x ⬎ 0.
冕 a dx ⫽ ᎏlnaᎏa ⫹ C
冕a
Luego ᭙x 僆 ⺢, x ⫽ 0:
1
ᎏᎏ dx ⫽ ln⏐x⏐⫹ C
x
冕 cos xdx ⫽ sen x ⫹ C
冕 cos u ⭈ u' ⭈ dx ⫽ sen u ⫹ C
冕 sen xdx ⫽ ⫺cos x ⫹ C
冕 sen u ⭈ u' ⭈ dx ⫽ ⫺cos u ⫹ C
1
冕ᎏ
ᎏ dx ⫽ tg x ⫹ C
cos x
1
冕ᎏ
ᎏ ⭈ u' ⭈ dx ⫽ tg u ⫹ C
cos u
冕 (1 ⫹ tg x)dx ⫽ tg x ⫹ C
冕 (1 ⫹ tg u) ⭈ u' ⭈ dx ⫽ tg u ⫹ C
⫺1
冕ᎏ
ᎏdx ⫽ cotg x ⫹ C
sen x
⫺1
冕ᎏ
ᎏ ⭈ u' ⭈ dx ⫽ cotg u ⫹ C
sen u
1
冕ᎏ
ᎏ dx ⫽ arc tg x ⫹ C
1⫹x
1
冕ᎏ
ᎏ ⭈ u' ⭈ dx ⫽ arc tg u ⫹ C
1⫹u
⫺1
冕ᎏ
ᎏ dx ⫽ arc cotg x ⫹ C
1⫹ x
⫺1
冕ᎏ
ᎏ ⭈ u' ⭈ dx ⫽ arc cotg u ⫹ C
1⫹u
1
冕ᎏ
dx ⫽ arc sen x ⫹ C
⫺苶x苶
兹1苶苶
1
冕ᎏ
⭈ u' ⭈ dx ⫽ arc sen u ⫹ C
⫺苶u苶
兹1苶苶
⫺1
冕ᎏ
dx ⫽ arc cos x ⫹ C
⫺苶x苶
兹1苶苶
⫺1
冕ᎏ
⭈ u' ⭈ dx ⫽ arc cos u ⫹ C
⫺苶u苶
兹1苶苶
n⫹1
n
1
La integral de ᎏᎏ
x
Para x ⬎ 0:
1
ᎏᎏ dx ⫽ ln x ⫹ C
x
冕
Para x ⬍ 0:
1
⫺dx
ᎏᎏ dx ⫽ ᎏᎏ ⫽ ln (⫺x) ⫹ C
x
⫺x
冕
冕
冕
x
x
x
x
2
2
2
2
2
2
2
n
un⫹1
⭈ u' ⭈ dx ⫽ ᎏᎏ ⫹ C
n⫹1
u
u
u
au
⭈ u'dx ⫽ ᎏᎏ ⫹ C
ln a
2
2
2
2
2
2
2
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