# tabla de integrales pdf - table de integrales online completa

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∫ sen (u ) du = − cos( u ) + C

6

7

a 2 + u 2 du = 2

a + u2 −

2 a4  ln u + a + u 2  + C  8 

)

(

)

(

du

)

a2 + u2 a2 + u2 du = − + ln u + a 2 + u 2 + C 2 u u du = ln u + a 2 + u 2 + C a 2 + u2 u 2 du u 2 a2 = a + u 2 − ln(u + a 2 + u 2 ) + C 2 a2 + u2 2

a2 + u2 a + a2 + u2 du = a 2 + u 2 − a ln +C u u

8

3

1 a2 + u2 + a = − ln +C 27 ∫ a u u a2 + u2

2

(a u + 2u )

(

u 2 a2 a + u 2 + ln u + a 2 + u 2 + C 2 2

2 2 2 ∫ u a + u du =

cos(u )

2

u = arc sen ( ) + C a a −u

du

2

19

∫a

2

du 1 u+a = ln +C − u 2 2a u − a du 1 u −a = ln +C 20 ∫ 2 u − a 2 2a u + a

17

du 1 u ∫ a 2 + u 2 = a arc tg( a ) + C du 1 u = arc sec( ) + C 18 ∫ 2 2 a a u u −a

16

du

2

2

2

a2 − u2

du

2

du

=−

a2 − u2 +C a 2u

1 a2 − u2 + a = − ln +C a u a −u

a −u 1 2 u du = − a − u 2 − arc sen ( ) + C u2 u a u 2 du u 2 a2 u 2 =− a − u + arc sen ( ) + C 2 2 a a2 − u2

2

40

∫u

2

3

2

2

2

4

2

2

( 2u − a u ) u − a a − ln u + u 2 − a 2 + C u − a du = − 8 8

2 2 3/ 2 ∫ (a + u ) du = −

∫u

=−

a 2 − u2 a + a2 − u2 du = a 2 −u 2 − a ln +C u u

du

(2u 3 − 5a 2 u ) a 2 − u 2 3a 4 u + arc sen ( ) + C 8 8 a du u = +C 38 ∫ 2 (a − u 2 ) 3 / 2 a 2 a 2 − u 2 u a2 2 2 2 2 2 2 39 ∫ u − a du = 2 u − a − 2 ln u + u − a + C

37

36

∫ sen(u) = ln sen(u) − sen (u ) + C 35 ∫ u

1

∫ sec( u ) du = ln sec(u ) + tg(u) + C 34 ∫

14

15

33

∫ cot g(u ) du = ln sen (u) + C

13

32

∫ tg (u ) du = ln sec( u ) + C

12

∫u

28

2

∫ sec (u ) du = tg(u ) + C

8

a2 + u2 +C 2 a 2u a2 + u2 du u 2 = +C 9 ∫ cos sec (u ) du = − cot g (u ) + C 29 ∫ 2 (a + u 2 ) 3 / 2 a 2 a 2 + u 2 u 2 a2 u 2 2 2 10 ∫ sec(u ) tg(u ) du = sec(u ) + C 30 ∫ a − u du = 2 a − u + 2 arc sen( a ) + C cot g( u ) 1 u a4 u du = − +C 11 ∫ 31 u 2 a 2 −u 2 du = (2u 2 − a 2 ) a 2 − u 2 + arc sen ( ) + C ∫ sen ( u ) sen ( u ) 8 8 a

cos(u ) du = sen (u ) + C

u

26

25

∫ a du = In(a ) a

5

1

24

u

+C

u

∫ e du = e

23

22

4

+C

+C

21

u

n +i

v du

du = 1n u + C u

n

∫ u du = n + 1u

1

∫ u dv = uv − ∫

3

2

1

Tabela de Integrais

2

2

u −a du

2

du 2

=

u2 − a2 +C a 2u u

u du

∫ a + bu

2

2b 3

[(a + bu ) − 4a (a + bu ) + 2a =

du

udu

2

2

∫ u (a + bu )

du

∫ (a + bu ) =

ln

1 1 a + bu − ln +C a (a + bu ) a 2 u

2

b

a + bu +C u a 1 = 2 + ln a + bu + C b (a + bu ) b 2

1

∫ u (a + bu ) = − au + a 2

2

]+ C

77

60

∫u

n

a + bu du =

b(2n + 3)

2 u n (a + bu )3 / 2 − na ∫ u n −1 a + bu du

[

] 80

79

+ c, se a > 0

a + bu a + bu b du du = − + ∫ u2 u 2 u a + bu

a + bu + a

a + bu − a

ln

59

a

1

78

du =

a + bu du du = 2 a + bu + a ∫ u u a + bu

a + bu

du

2

(u )du =

3

3

2

3

3

tg ( u ) + ln cos( u ) + C 2

2

[2 + cos (u)]sen (u ) + C udu =

2

[2 + sen (u)]cos( u) + C

(u )du = − cot g (u ) − u + C

( u )du = −

2

∫ tg (u )du =

∫ cos

∫ sen

3

1 1 u + sen ( 2u ) + C 2 4

( u )du = tg (u ) − u + C

2

∫ cot g

∫ tg

∫ cos

∫ sen

n

n

(u )du =

(u )du = −

3

sen n −1 (u ) cos( u ) n − 1 + sen n −2 ( u )du n n ∫

∫ cot g (u )du = −

n

( u ) du =

tg(u ) sec n −2 (u ) n − 2 + sec n −2 (u ) du n −1 n −1 ∫

∫ cos(au) cos(bu)du =

∫ sen(au) sen(bu)du =

sen (a − b)u sen (a + b)u + +C 2 (a − b ) 2(a + b)

sen (a − b) u sen (a + b)u − +C 2(a − b) 2 (a + b )

du cot g( u ) n−2 du =− + n (u ) ( n − 1)sen n −2 (u ) n − 1 ∫ sen n −2 ( u )

∫ sen

∫ sec

∫ cos

cos n −1 (u )sen (u ) n − 1 + cos n −2 (u )du n n ∫ tg n −1 (u ) 75 tg n ( u )du = − ∫ tg n −2 (u )du ∫ n −1 cot g n −1 (u ) 76 cot g n (u ) du = − − ∫ cot g n −2 (u ) du ∫ n −1 74

73

70

∫u

u n du 2u n a + bu 2na u n −1du = − ∫ b(2n − 1) b(2n + 1) a + du a + bu

cot g 2 ( u ) − ln sen ( u ) + C 2 sec( u ) tg ( u ) ln sen (u ) + tg ( u ) 71 sec 3 ( u )du = − − +C ∫ 2 2 du cot g (u ) ln cos sec( u ) − cot g ( u ) 72 ∫ =− + +C sen 3 ( u ) 2sen ( u ) 2

69

68

67

66

65

64

u − n du a + bu b(2n − 3) u − n +1du =− − n −1 a (n − 1) u 2a (n − 1) ∫ a + bu a + bu 1 1 2 63 ∫ sen (u )du = u − sen (2u ) + C 2 4

62

61

58

57

 u 2 du 1 a2  = a + bu − − 2a ln a + bu  + C 2 3 ∫ (a + bu ) b  a + bu  2 32 54 ∫ u a + bu du = (3bu − 2a )(a + bu ) + C 15b 2 udu 2 = 2 (bu − 2a ) a + bu + C 55 ∫ 3 b a + bu 2 u du 2 56 ∫ = (8a 2 + 3b 2 u 2 − 4abu) a + bu + C 3 a + bu 15b 53

52

51

50

du 1 u = ln +C 49 ∫ u (a + bu ) a a + bu

48

2

) ln a + bu

u2 − a2 u2 − a2 + ln u + u 2 − a 2 + C du = − 2 u u du = ln u + u 2 − a 2 + C u2 − a2 u 2 du u a2 = u 2 − a 2 + ln u + u 2 − a 2 + C 2 u2 − a2 2

u2 − a2 a du = u 2 − a 2 − a arc cos( ) + C u u

∫ (u

∫u

=− +C 3/ 2 − a2 a2 u2 − a2 udu 1 47 ∫ = (a + bu − a ln a + bu ) + C a + bu b 2 46

45

44

43

42

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