tabla integrales
TRANSCRIPT
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= =
+ +∫ ∫