Tabla integrales

1. Tipos FFFFoooorrrrmmmmaaaassss
SSSSiiiimmmmpppplllleeee CCCCoooommmmppppuuuueeeessssttttaaaa
Tipo potencial a ¹ -1
x
∫ =
+
+
1
1
a
x dx
a
× ¢ =
+
1
f
a ∫ +
1
a
f f dx
a
a
∫ = 1
( 2 )31
x 4 dx x 5 ( )( ) 5
2 30 1
2 1 1
x x
31
x x x dx
+ +
∫ + + + =
Tipo logarítmico
∫ = 1
dx L x
x
¢
∫
f =
dx L f
f
3 1
dx 3 dx 3L x
x x
∫ = ∫ =
2
= 3
+
3 1
3
8
8 3
+ ∫ x
dx L x
x
Tipo exponencial
∫ exdx = ex
a
La
a dx
x
∫ x =
∫ e f × f d¢ x = e¢
∫ f × ¢ =
a
¢
a f dx La
2 1 2 1 2 1 1 1
∫ e x + d x = ∫ e x + × d x = e x +
2 2
+
2 1
2 1 2 1 1 1
3 3
x x e
∫ + = ∫ + × =
x
dx d x
2 2 ln 3
Tipo seno ∫ cos xdx = senx ∫ cos f × f d¢ x = senf
1 1
∫ s e n 2 x dx = ∫ s e n 2 x × 2 dx = - cos 2
x
2 2
Tipo coseno ∫ senxdx = -cos x ∫ senf × f d¢ x = -cos f ∫ (2x + 1)× cos (x2 + x + 1)dx = s e n (x 2 + x + 1)
Tipo tangente
∫ xdx = tgx sec2
∫ ( + tg x)dx = tgx 1 2
∫ = cos2
dx tgx
x
1
∫ f × f d¢ x = tgf sec2
∫ ( + tg f )× f d¢ x = tgf 1 2
f =
dx tgf
f
¢
∫ cos2
∫3sec2 x dx = 3∫sec2 x dx = 3tan x
∫ dx = ∫ 2
x dx = x
7
2
7 sec 7 tan
cos
x
∫ (5 + 5 tan2 x)dx = 5∫ (1+ tan2 x)dx = 5 tan x
Tipo arco seno
=
1
∫ 1 2
dx arcsenx
x
-
x
dx arcsen
a
1
∫ 2 2
a x
=
-
f =
-
dx arcsenf
f
¢
∫ 1 2
f
¢
f =
-
dx arcsen
a
∫ 2 2
a f
2 2
x x
∫ ∫
= =
dx dx x
( )
2
- -
4 2 2
arcsen
1 1
x x
Tipo arco tangente
=
1
+ ∫ 1 2
dx arctgx
x
x
1 1
2 2 =
+ ∫
arctg
a
a
dx
a x
¢
f =
+
∫ 1 2
dx arctgf
f
f
¢
f 1
2 2 =
+
arctg
a
a
dx
a f
∫
1 1 1 1
+ + ∫ ∫
= =
dx dx x
2 2
arctg
3 3 x 3 1 x
3