Tipos FormasFormasFormasFormas

SimpleSimpleSimpleSimple CompuestaCompuestaCompuestaCompuesta Tipo potencial a ≠ -1

∫ +=

+

1

1

a

xdxx

aa

∫ +=′⋅

+

1

1

a

fdxff

aa

4 51

5x dx x=∫ ( )( ) ( )312

3021

2 1 131

x xx x x dx

+ ++ + + =∫

Tipo logarítmico

xLdxx

=∫1

fLdxf

f =′

∫ 3 1

3 3dx dx L xx x

= =∫ ∫

23

3

3 18

8 3= +

+∫x

dx L xx

Tipo exponencial

xx edxe =∫

La

adxa

xx =∫

∫ ′=′⋅ edxfe f

La

adxfa f ′

=′⋅∫

2 1 2 1 2 11 1

2 2x x xe d x e d x e+ + += ⋅ =∫ ∫

2 1

2 1 2 11 13 3

2 2 ln 3

++ += ⋅ =∫ ∫

xx x e

dx d x

Tipo seno

∫ = senxxdxcos ∫ =′⋅ senfdxffcos 1 1

s n 2 s n 2 2 cos 22 2

e x dx e x dx x= ⋅ = −∫ ∫

Tipo coseno

∫ −= xsenxdx cos ∫ −=′⋅ fdxfsenf cos ( ) ( ) ( )2 22 1 cos 1 s n 1x x x dx e x x+ ⋅ + + = + +∫

Tipo tangente

tgxxdx =∫2sec

( ) tgxdxxtg =+∫21

tgxdxx

=∫ 2cos

1

tgfdxff =′⋅∫2sec

( ) tgfdxfftg =′⋅+∫21

tgfdxf

f =′

∫ 2cos

2 23sec 3 sec 3tanx dx x dx x= =∫ ∫

22

77 sec 7 tan

cos= =∫ ∫dx x dx x

x

( ) ( )2 25 5 tan 5 1 tan 5 tanx dx x dx x+ = + =∫ ∫

Tipo arco seno

arcsenxdxx

=−∫ 21

1

a

xarcsendx

xa=

−∫ 22

1

arcsenfdxf

f =−

′∫ 21

a

farcsendx

fa

f =−

′∫ 22

( )2

4 22

2 2arcsen

1 1

x xdx dx x

x x= =

− −∫ ∫

Tipo arco tangente

arctgxdxx

=+∫ 21

1

a

xarctg

adx

xa

1122

=+∫

arctgfdxf

f =+

′∫ 21

a

farctg

adx

fa

f 122

=+′

∫

2 2

1 1 1 1arctg

3 3 3 1 3dx dx x

x x= =

+ +∫ ∫