Integrales Calculo.pdf

8/16/2019 Integrales Calculo.pdf

1/40

INSTITUTO POLITÉCNICO NACIONALEscuela Superior de Cómputo

“ Lista de Integrales ”

Alumno:Yosef Israel Gutiérrez Moreno

Grupo:1CV9

Profesor:Alfredo Guzmán Rangel

Materia:“Calculo”

Semestre:14/2


2/40

2LISTA DE INTEGRALES1)

=6

2.

(√ )

√ =223

22√3 3)

3√

√ 4

= 3√ √ 4 = 3− /4=3− /14 /

=3 /1/214 /5/2

=6/ √

4. ∫√ = =· ∫ 2 = =√ 2∫

=2

=√ 2+


3/40

3=√ 2 6. ∫√

√ = = − =34 =43 =43

8.∫ u=5x; du=5 dx

= ∫ =

9.

5 =5

= 5 →5=

→ 5=15 =15 = 55 11. ∫ =∫∗ ∗=∫ ∗ == =ln

=1

∗ = 12.3 =3 =3

3=


4/40

4= 3

=13

=13 =13 cot =cot33 14.

3 7 =3 7 =3 →3=

→ 13 =

13

=13ln|| =13ln|3 7| 15.-

∫ − u=1-x= ∫ − =

= | |

17. ∫tan2 =2 =2 =12 tan∫u12 ∫tan2

12 tan


5/40

5∫tan2 ∫ sincos2

=cos = sin=1sin ∫sin 1sin∫ 12

2=cos2

2 =cos22

. = == ||= | |

=5 7 → =55= = → = 19. 3= tan3 =13 tan =13cos=13 1ℎ ℎ= log3= 13logcos= 13ln|cos3| . = 3 & =3 ; ℎ=c& = sin

ɵ∗ɵ∗ ɵ u= ɵ du=

ɵ∗ ɵ

=2 = ɵ

23.


6/40

6 454 44

=4 =4 =4 =4 14 4 14ln| | 4ln| |

14ln| 4 | 4ln4 24)cos = =3 =3 u=sen x =cos

25.

∫ =

=∫

=∫ 1 = =∫ = = + = = 27. ∫ √ + √ 2 3=

2 3=2 3

−

=23 =4 4=

− 4=14

− =1412

=24

=122 3

=12 2 3


7/40

728.-∫ + =∫ 1− =∫ − = ∫ − = = = 1 = √

=3 =3 3=

29.∫ U=sen(x), du=cos(x) dx

=∫ = = - 30.

= = → − = − = −2 =12 32.

∫ =∫ = +=∫ =

=cot =1 =

33. 1 = 1 =


8/40

8= 1− = − =12=2=2 1=2 1

35.

√ 2 1 =2 1 =2 →2=

→ −⁄2=12 −⁄ =121

2=⁄

=√ 2 1 36-∫ + = =

=

= = = | | 38.


9/40

9∫ tan 1(cos)

=tan =sec=cos √ 1coscos √ 1 = 1 =1 =1

√ 1

√ +12 1=

tan1+12 1=2 13

.∫ + =∫ =∫− =− = +=2 3 → =3 26= 2 √

u=arcsenx

du= √ −

=2 = 43)


10/40

10cot1 = = =2

=

2

= cot =11 44.

√1

=arccos , = √1

1 =3 = 2 45)

cot1 = = 2 = 2 = cot

=11 46. ∫ += =∫ + =∫ +2 = 1 =∫ =2 =∫ = =∫ + = | 1| 48.

∫

+


11/40

11cos 2sin 3 u=2sinx 3 =2cos

2=cos 2=2=12 =12ln =12ln 2sin 3

49-∫ = ∫ = ∫ = | | = |

50.∫2 1 =2∫ 1 U= +1 , du= 2x dx

=

∫du

= + c

= ( 1 + c51.

= = 1 = = 1 =

= =

= = =

=


12/40

12= =3

=3

52.-∫ + =tan− =1 1 = = ln= lntan− 53. ∫ +=∫ =ln =ln3 1 =3 tan1

=3

3=1

54. = =

= = =4 =4 56.

cos22 3 2=2 3 2


13/40

13=6 2 →6= 2 →6=16

=16ln|| =16ln|2 3 2| 57.-

∫ = ==

= = 59)

∫ ∫

∫+

1 1

∫2=2 . = = =2=12 → =12 2 =

61.

cos = = = . =

U=

Du= =

=


14/40

14= = 64)

∫ ∫ ∫ +1 1 ∫ = =1

4

65.

3

=3 =3ln3

1ln3ln3 1ln3ln3 =1ln3ln3

∫ 1ln3 =1ln3 11ln3 1 3 +1ln3 1 ln3

3ln3 166)


15/40

15− =3=13 =13 =1

3−

= 3 = 3 67. ∫ = ∫ ∫

=5 =∫ ∫ =5 =∫ ∫= = ∫ =5 = ∫ =5 = ∫ = = = =

69. ∫ − = 2

= 2 = 2

= 2 =lnln 2=ln lnln ln2=ln lnln ln2 =ln ln2

70.-∫ + =∫ + =∫ =∫ = ∫ = | |

=


16/40

16= =

= 71.∫ + U= 2x, du=2dx

= ∫ + S= 2, ds= du

=

∫

=

= log( 2 = log( 2 72.

1 2

=1 ; =√ 2 =√ 2 →√ 2= →1√ 2 1 =1√ 21−

=1√ 2

−√ 2

73.- ∫√ − =∫√ ·√ ·√ =√ 3 =√ 3 →√ 3= √ 3√11

= √ 3 · √1=

13√1=1√ 3sin− C


17/40

1774.√16 9=13√ =13 =13 394

√=

=16, =4: =9, =3 75.√9 =9 ; =3 = ; = =1 =1

3 377.9 4 =3 ; =2

=3 →3=

13 =13 1312arctan32 =16 arctan32 78.-

= =

= =

[ ]


18/40

18

| | | |

| | | | | |

80.

∫√ =asec =tansec = sec =atan =arcsec

12∫sec sectansec tan

s=tanu secu ds=sectansec 1∫1s =


19/40


20/40

2087)

√3 5=1√ 3

1 153

=1√ 5

1√1

= 1√ 5

= 53√ 5

= 53 = 53 90. ∫ −√ − cos−√1 =cos−√1 √1 =cos−√1 1=cos−√1 1− =cos− , =1

=√1, = 2

=√1, 2= − 2 = 12 − =21212=12cos− 221 =12cos− 1

91.-∫ −+ = ∫ − = ∫ + =∫ = ∫ = 1 =∫ = ∫ = = =

=

= =


21/40


22/40

2295 .∫ +=arctanc Se utiliza la formula += = , = = ; =, =

96.cos √ = =cos = −cos

= − =13 =3=3 =3√

98.

2√ 1 :

2 =2 →2√ 1

= 1 = 2 → − = 2 = 2 1 99.-

∫ = = ∫ =


23/40

23

− −

= 101.

∫2sin 3cos =? 122.

∫ 2√ ∫ = = 2 ∫1√

√

= . = ==

103.∫ − +=∫√ −√ + =√ ∫ + =

√ ∫ + =√ ∫ + =√ ∫ + =√ tan− =

√ =√ 3 √ , =√ 3 ; = , =

6 9 9 5

34


24/40

24= 3 =

∫ −=

ln−+

=12 2ln 3 232 =

106)

2 2 1= = =

111. ∫ ++ − 7 16 1=7 12 1 3 1 7 12 13 1= 2 13 1 7 1=3 12 1 7 1=3 2

7 1=3 2 3 2 =7 =1 =1 =2 7 12 13 1=12 123 1

7 12 1 3 1=12 123 1 =2 12 3 1


25/40

25=2 1, =3 1 =2 , =3

2= ,3=

2 23=2 23=12 23 =12ln| |23ln| |=12ln 2 123ln 3 1 =23ln 3 112ln 2 1 112.-∫ −− + =∫ −− + = − +− + = ∫ − + =2∫ − + = √ √ 39√ √ =

√ 39 √ 39√ √ = √ √ 39√ √ ) = √ 39 √ 39√ √ = ln √ 39 √ 39√ √ = ln √ √ 10 1 = ln√ √ 10 1

117.√ 2 =ln 2 .√ = √ √ =

√

= || = = = =4 13 → =4 4 , 1 ,4

= 1 ,4 1=


26/40

26124.∫ −√ + − = ∫√ = 2√ = √ = √ 1166 3 129)

= cos= cos = = = = = = cos

132. ∫ln 1 ln1 =ln1 , = =1 , = ln1 = ln1 1 = 1 = 1


27/40

27= ln1 1 = ln1 1= ln1

= ln1 = ln1 ln1= 1ln1 133.-∫ = + ∫ + =∫ + = + ln++ C = =

=

135.

= =√1

= =2 →2 2√1 =2 2√1 =2 =12 = √1 = 1 →2 [2 1 1 2] =2 [2 1 12 1 ] ó = 1 =

=

1 :

= =

= 1


28/40

28= =1 22 =212 2 =214 2=12 12 2

=12 :=→ = √1= ℎ :

2 [2 11212 1 ]=2 2 1 14 14 1 =2 4 1 14 142 1 1

136.-

∫log 1 =∫ =∫

= ln1 = =+ = = ln1∫ + = ln1 2 1

= ln1 2 11

1

= ln1 21 1 2 1 = ln1 2tan− 2 1 = ln1 2tan− 2 137. ∫arctan√ =arctan√ ∫√ + = √ =

=12√ 1 =


29/40

29√ = =, =2 arctan√ 12 2 1 = arctan√ 1

= arctan√ 111 =

arctan√ 1 = arctan√ arctan= arctan√ √ arctan√ 138.√ √

= √ =√

=1 1√ =−

=1√ 1 =2√ =2√ √ 2√ √ 1 =2√ √ 2√ √ 1 =2√ √ 2(√ 1 ) 140.

= = = =

→ = 1 22 =12⌈ 2 =12[ 12 2 ]=12[ 22 ] =12

→2 12


30/40

30=2 12 12 2 122 =2 2 4 2 =42 4 2 =4 24 2 143.∫x tan− 1

=√1 =√ − ∫u tan−u =tan−u = =1 1 =2

12tan−u12∫1 12∫ 1 1

12tan−uu212tan−u =12tan− 1 1 . = = =√

= √ = || = → =1√1 , =− → =


31/40


32/40

32 csc = cos/ ℎ= ℎ=cos 1ℎ ℎ =1ℎcsc=√ 1

151. ∫√ + = ∫ =∫ =| |

√ = =√ + = = =√ + =

153. ∫ + + + 1 3 5= 1 3 5

= 3 5 1 5 1 3

= 8 156 54 3 = 8 156 54 3 = 8 6 4 =0 8 6 4 =1

15 5 3 =0

=18, =34, =58


33/40

3318 134 358 5 =18 134 358 5=

18 1

34 3

58 5==18ln 134ln 358ln 5=18 ln16ln 35ln 5=18ln 35 1

156.

1 2

11 2= 1 1 2 1= 1 2 2 1 =1 = 1 =2 =1 3 2 22 =1 2 2 =1 2 2 1=1

2 = 2 = 1 1 1 2= ln| 1| 1 1ln| 2| =1 1ln 12

157.-∫ −− + =∫ −−

=22

23

2 = 31 2 21 2 21 =21 31 2 21 =2ln 3∫ 2∫ … 3∫ = 3= …=2ln2ln = − ln

−


34/40

34

161.

2 3 312 5

2 3 312 5= 1 2 5 2 3 3=2 5 1 2 5 =23 3 → =2 2 = 3 5 = 3 = 1

=3 = 213 22 5

ln| 1| 2 22 512

=ln2 5

1 12

164.

∫ 3 74 4


35/40

35

=

42 1

12

−2

196.-∫ =∫ = ∫ 1 =∫ ∗ = ∫ ∗∫ =∫ ∗∫ = ∫ = ∫ =+ = = = = =

= = =


36/40

36

198.

= = 1 = =

5 7

199.- ∫ =∫ = ∫ 1 = = = 1 = 1

= 13

= 3 =csc3 = 13 200.∫ =∫ +=∫ ∫ =∫ ∫ =

=414 2 = =1 cos22 201.

= = [1212cos2 ]=

1412cos2

14 2


37/40

37=4 cos22 8 cos4 8 =14

12

cos218

18

cos4 =2 =4 =2 =4

2= 4= 14 12 cos218 18 cos4 14

1212 cos

18

1814 cos

=14 14 218 132 4 =38 14 2132 4 203.

= 1 22 1 22 116218 2 116 1162 =116 2

2 =1 44 = 1 2 4 44 14 4 =14 4 4 =1 cos82

12cos8 12 =12 cos8 2


38/40

3818 cos =18 = 1418 82 =132 816

12 =2 12 4 =12 4 =18 4 14 =4 18 2 =

18 2 2 =1 42 12 4 =18 4 12 =2 116 =16

→31281128 411024 8 →11283 4sin88

206.

∫cot− cot x ( cos² x /sen² x )cot x ( (1 – sen² x)/sen² x )((cot x/sen² x) – cot x)

∫ cot³ (x) dx = ∫ ((cot x/sen² x) – cot x) dx =∫ (cot x/sen² x) dx – ∫ cot x dx =

(-1/2) cot² x – In(sen x) + C


39/40


40/40

40=6 = =∫ · ∫=∫ ∫ = ∫

=− ∫ =2 =2 = =− ∫ · =− ∫ =− =− 220.-∫ + =∫ + = 1 = =− = 1 1 = 1 1 =1 1

Documents

Integrales Calculo.pdf