formulario de derivas y integrales

1
1 ) sec ( . 23 1 ) (arctan . 21 1 ) ( . 19 tan sec sec . 17 sec tan . 15 cos . 13 . 11 log log . 10 1 . 9 1 . 7 . 6 . 5 ) ( . 3 0 . 1 2 2 2 2 1 v v dx dv v arc dx d v dx dv v dx d v dx dv arcsenv dx d dx dv V v v dx d dx dv v v dx d dx dv v senv dx d dx dv e e dx d a dx dv v e v dx d dy dx dx dy dx du c c u dx d a nx x dx d a dx du v dx dv u uv dx d dx dw dx dv dx du w v u dx d c dx d V V n n vdu uv udv c a v arcsen a v a v dv v a c a v arcsen v a dv c a v a v a a v dv c v v c v v vdv c v c senv vdv c v vdv v c v vdv c senv vdv c e dv e c v v dv c x dx dw dv du dw dv du V V . 24 2 2 . 22 . 20 ln 2 1 . 19 cot csc ln cot csc ln csc . 17 csc ln ln cot . 15 csc cot csc . 13 cot csc . 11 cos . 9 . 7 ln . 5 . 3 ) ( . 1 2 2 2 2 2 2 2 2 2 2 c a v arc a a v v dv c a v v a a v v dv a v c a v v a v dv c v a v a a v a dv a c a v a a v dv c v v vdv c v c v vdv c v vdv v c v vdv c v senvdv c a a dv a c n v dv v dv a adv V V n n sec 1 . 25 ln 2 2 . 23 ln . 21 ln 2 1 . 19 arctan 1 . 18 tan sec ln sec . 16 sec ln cos ln tan . 14 sec tan sec . 12 tan sec . 10 cos . 8 ln . 6 1 . 4 . 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 Fórmulas de Integración Fórmulas de Derivación 1 ) csc ( . 22 1 ) cot ( . 20 1 ) (arccos . 18 cot csc csc . 16 csc cot . 14 cos . 12 ln . 11 1 ln . 8 . 7 . 6 . 4 1 . 2 2 2 2 2 2 1 v v dx dv v arc dx d v dx dv v arc dx d v dx dv v dx d dx dv v v v dx d dx dv v v dx d dx dv senv v dx d dx dv a a a dx d dx dv v v dx d v dx dv u dx du v v u dx d dx dv nv v dx d dx dv c cv dx d x dx d V V n n Nombre: senAsenB B A B A senAsenB B A B A A senB B senA B A sen A senB B senA B A sen B senB B B B cos cos ) cos( . 12 cos cos ) cos( . 11 cos cos ) ( . 10 cos cos ) ( . 9 cos tan . 4 sec 1 cos . 2 Identidades Trigonométricas ) tan ( sec ) sec ( tan ) cos ( : 2 2 2 2 2 2 z a a u z a u z a u a z a u z a u a senz a u rica trigonomét n sustitució Para [ ] [ ] [ ] [ ] ) ( ) ( 2 1 cos . 19 ) ( ) ( 2 1 cos . 18 ) cos( ) cos( 2 1 cos cos . 17 ) cos( ) cos( 2 1 . 16 : B A sen B A sen AsenB B A sen B A sen B senA B A B A B A B A B A senAsenB diferentes ángulos Para cos 2 2 1 . 15 2 cos 2 1 2 1 . 14 2 cos 2 1 2 1 cos . 13 : 2 2 B senB B sen B B sen B B pares potencias Para cot 1 csc . 8 tan 1 sec . 7 1 cos . 6 cos cot . 5 cot 1 tan . 3 csc 1 . 1 2 2 2 2 2 2 B B B B B B sen senB B B B B B senB B. Limas

Upload: alvarorafaelerrasquin

Post on 18-Dec-2015

4 views

Category:

Documents


1 download

DESCRIPTION

formulario de integrales y derivadas

TRANSCRIPT

  • 1)sec(.23

    1)(arctan.21

    1)(.19

    tansecsec.17

    sectan.15

    cos.13

    .11

    loglog.10

    1.9

    1.7

    .6

    .5

    )(.3

    0.1

    2

    2

    2

    2

    1

    vv

    dxdvvarc

    dx

    d

    v

    dxdvv

    dx

    d

    v

    dxdvarcsenv

    dx

    d

    dx

    dvVvv

    dx

    d

    dx

    dvvv

    dx

    d

    dx

    dvvsenv

    dx

    d

    dx

    dvee

    dx

    da

    dx

    dv

    v

    ev

    dx

    d

    dydxdx

    dy

    dx

    du

    cc

    u

    dx

    da

    nxxdx

    da

    dx

    duv

    dx

    dvuuv

    dx

    d

    dx

    dw

    dx

    dv

    dx

    duwvu

    dx

    d

    cdx

    d

    VV

    nn

    vduuvudv

    ca

    varcsen

    ava

    vdvva

    ca

    varcsen

    va

    dv

    cav

    av

    aav

    dv

    cvvcvvvdv

    cvcsenvvdv

    cvvdvv

    cvvdv

    csenvvdv

    cedve

    cvv

    dv

    cxdx

    dwdvdudwdvdu

    VV

    .24

    22.22

    .20

    ln2

    1.19

    cotcsclncotcsclncsc.17

    csclnlncot.15

    csccotcsc.13

    cotcsc.11

    cos.9

    .7

    ln.5

    .3

    )(.1

    22222

    22

    22

    2

    ca

    varc

    aavv

    dv

    cavva

    avv

    dvav

    cavvav

    dv

    cva

    va

    ava

    dva

    ca

    v

    aav

    dv

    cvvvdv

    cvcvvdv

    cvvdvv

    cvvdv

    cvsenvdv

    ca

    adva

    cn

    vdvv

    dvaadv

    VV

    nn

    sec1

    .25

    ln22

    .23

    ln.21

    ln2

    1.19

    arctan1

    .18

    tanseclnsec.16

    seclncoslntan.14

    sectansec.12

    tansec.10

    cos.8

    ln.6

    1.4

    .2

    22

    222

    2222

    22

    22

    22

    22

    2

    1

    Frmulas de Integracin

    Frmulas de Derivacin

    1)csc(.22

    1)cot(.20

    1)(arccos.18

    cotcsccsc.16

    csccot.14

    cos.12

    ln.11

    1ln.8

    .7

    .6

    .4

    1.2

    2

    2

    2

    2

    2

    1

    vv

    dxdvvarc

    dx

    d

    v

    dxdvvarc

    dx

    d

    v

    dxdvv

    dx

    d

    dx

    dvvvv

    dx

    d

    dx

    dvvv

    dx

    d

    dx

    dvsenvv

    dx

    d

    dx

    dvaaa

    dx

    d

    dx

    dv

    vv

    dx

    d

    v

    dx

    dvu

    dx

    duv

    v

    u

    dx

    d

    dx

    dvnvv

    dx

    d

    dx

    dvccv

    dx

    d

    xdx

    d

    VV

    nn

    Nombre:

    senAsenBBABA

    senAsenBBABA

    AsenBBsenABAsen

    AsenBBsenABAsen

    B

    senBB

    BB

    coscos)cos(.12

    coscos)cos(.11

    coscos)(.10

    coscos)(.9

    costan.4

    sec

    1cos.2

    Identidades Trigonomtricas

    ) tan ( sec

    ) sec ( tan

    ) cos (

    :

    2 2

    2 2

    2 2

    z a a u z a

    u

    z a u a z a

    u

    z a u a senz a

    u

    rica trigonomt n sustituci Para

    [ ]

    [ ]

    [ ]

    [ ] ) ( ) ( 2

    1 cos . 19

    ) ( ) ( 2

    1 cos . 18

    ) cos( ) cos( 2

    1 cos cos . 17

    ) cos( ) cos( 2

    1 . 16

    :

    B A sen B A sen AsenB

    B A sen B A sen B senA

    B A B A B A

    B A B A senAsenB

    diferentes ngulos Para

    cos 2 2

    1 . 15

    2 cos 2

    1

    2

    1 . 14

    2 cos 2

    1

    2

    1 cos . 13

    :

    2

    2

    B senB B sen

    B B sen

    B B

    pares potencias Para

    cot 1 csc . 8

    tan 1 sec . 7

    1 cos . 6

    cos cot . 5

    cot

    1 tan . 3

    csc

    1 . 1

    2 2

    2 2

    2 2

    B B

    B B

    B B sen

    senB

    B B

    B B

    B senB

    B. Limas