Integrales inmediatas

TABLA DE INTEGRALES INMEDIATAS 1. 2. 3.

∫ du = u + c ∫ adu = au + c ∫ [ f (u ) + g (u )]du = ∫ f (u )du + ∫ g (u)du
u n +1 undu = + c , n ≠ −1 ∫ n +1 au a udu = +c ∫ ln a
u u ∫ e du = e + c

12. 13. 14. 15. 16. 17. 18.

4. 5.

∫ sec u tg udu = secu + c ∫ csc uc tg udu = − csc u + c ∫ tg udu = ln sec u + c ∫ c tg udu = ln sen u + c ∫ csc udu = ln csc u − c tg u + c ∫ sec udu= ln sec u + tg u + c

6. 7. 8. 9. 10. 11.

∫ u = ln u + c ∫ sen udu = − cos u + c ∫ cos udu = sen u + c ∫ sec udu = tg u + c∫ csc udu = −c tg u + c
2 2

du

a2 − u2 du 1 u 19. ∫ 2 = arctg + c 2 a +u a a du 20. ∫ = ln u + u 2 ± a 2 + c 2 2 u ±a du 1u−a 21. ∫ 2 = ln +c 2 u −a 2a u + a

∫

du

= arcsen

u +c a

IDENTIDADES ALGEBRAICAS 1. 2. 3. 4. 5. 6. 7. 8.IDENTIDADES TRIGONOMETRICAS

aman = am+ n am = am−n n a

(a )
m

m n

= a mn

a n = n am 1 a−n = n a logb 1 = 0
logb b n = n1 sen θ 1 2. secθ = cosθ sen θ 3. tgθ = cosθ 1 4. c tg θ = tg θ
1.

cscθ =

sen 2 θ + cos 2 θ = 1 2 2 6. 1 + tg θ = sec θ5.

b log b n = n 2 2 2 9. (a ± b ) = a ± 2ab + b
10. 11. 12.

(a ± b )3 = a 3 ± 3a 2b + 3ab 2 ± b3 a 2 − b 2 = (a + b )(a− b ) a 3 ± b 3 = (a ± b )(a 2 ab + b 2 )

1 + c tg 2 θ = csc 2 θ 8. sen 2θ = 2 sen θ cosθ 2 2 9. cos 2θ = cos θ − sen θ
7.