Fórmulas de Cálculo Diferencial e Integral

Primitivas de funciones de x

Primitivas de funciones de x

[ ] 0d

cdx

= Cxdx +=∫

[ ] 1d

xdx

= Cxkdxkdxk +== ∫∫

[ ]( ) ( ) ( ) ( ) ( ) ( )d

f x g x f x g x g x f xdx

′ ′= + ∫∫∫ ±=± dxvxdudxvu )(

[ ]2

( ) ( ) ( ) ( ) ( )

( ) ( )

d f x g x f x f x g x

dx g x g x

′ ′ −=

1

1

1

−≠++

=+

∫ mCm

xdxx

mm

1n ndx nx

dx

− = Cxdxx +=∫−

ln1 1

lndx x cx

= +∫

[ ] cosd

sen x xdx

= Cedxe

xx+=∫

[ ]cosd

x sen xdx

= − Ca

adxa

x

x+=∫ ln

[ ] 2tan secd

x xdx

= Cxdxxsen +−=∫ cos

[ ] 2cot cscd

x xdx

= − Cxsendxx +=∫ cos

[ ]sec sec tand

x x xdx

=

Cxtgdxxtg

x

dxdxx

+=+

==

∫

∫∫

)1(

cossec

2

2

2

[ ]csc csc cotd

x x xdx

= −

Cxgdxxg

xsen

dxdxxec

+−=+

==

∫

∫∫

cot)cot1(

cos

2

2

2

x xde e

dx =

2sec sec

cos

sen x dxx tg x dx x C

x∗ = = +∫ ∫

lnx xda a a

dx =

2

cos cot

coscos

ec x g x dx

x dxec x C

sen x

∗ =

= − +

∫

∫

[ ]1

lnd

xdx x

= Ca

xarctg

axa

dx+=

+∫1

22

[ ]1

logln

a

dx

dx x a= C

a

xarcsen

xa

dx+=

−∫ 22

C

a

xarc

axax

dx+=

−∫ sec

1

. 22

2cot d cot Cθ θ θ θ= − − +∫

2tan d tan Cθ θ θ θ= − +∫

Integración por partes:

Recuerda: ´du u dx=

u dv u v v du= −∫ ∫

2 2a x− 2 2

a x+ 2 2

x a−