Integrales
Enviado por juanito123RCC • 1 de Abril de 2013 • 798 Palabras (4 Páginas) • 265 Visitas
Anexo D
Tabla de Integrales
(PUEDE SUMARSE UNA CONSTANTE ARBITRARIA A CADA INTEGRAL)
1.
Z
xn dx =
1
n + 1
xn+1 (n 6= −1)
2.
Z
1
x
dx = log | x |
3.
Z
ex dx = ex
4.
Z
ax dx =
ax
log a
5.
Z
sen x dx = −cos x
6.
Z
cos x dx = sen x
7.
Z
tan x dx = −log |cos x|
8.
Z
cot x dx = log |sen x|
9.
Z
sec x dx = log |sec x + tan x| = log
¯¯¯¯
tan
µ
1
2
x +
1
4
¼
¶¯¯¯¯
227
228 Tabla de Integrales
10.
Z
csc x dx = log |csc x − cot x| = log
¯¯¯¯
tan
1
2
x
¯¯¯¯
11.
Z
arcsen
x
a
dx = x arcsen
x
a
+
p
a2 − x2 (a > 0)
12.
Z
arccos
x
a
dx = x arccos
x
a
−
p
a2 − x2 (a > 0)
13.
Z
arctan
x
a
dx = x arctan
x
a
−
a
2
log
¡
a2 + x2¢
(a > 0)
14.
Z
sen2 mx dx =
1
2m
(mx − senmxcosmx)
15.
Z
cos2 mx dx =
1
2m
(mx + senmxcosmx)
16.
Z
sec2x dx = tan x
17.
Z
csc2x dx = −cot x
18.
Z
senn x dx = −
senn−1 x cos x
n
+
n − 1
n
Z
senn−2 x dx
19.
Z
cosn x dx =
cosn−1 x sen x
n
+
n − 1
n
Z
cosn−2 x dx
20.
Z
tannx dx =
tann−1x
n − 1
−
Z
tann−2x dx (n 6= 1)
21.
Z
cotnx dx =
cotn−1x
n − 1
−
Z
cotn−2x dx (n 6= 1)
22.
Z
secn x dx =
tan x secn−2 x
n − 1
+
n − 2
n − 1
Z
secn−2 x dx (n 6= 1)
23.
Z
cscnx dx =
cot x csc n−1x
n − 2
+
n − 2
n − 1
Z
cscn−2x dx (n 6= 1)
24.
Z
senh x dx = cosh x
25.
Z
cosh x dx = senh x
229
26.
Z
tanh x dx = log |cosh x|
27.
Z
coth x dx = log |sen hx|
28.
Z
sech x dx = arctan (senh x)
29.
Z
csch x dx = log
¯¯ ¯
tanh
x
2
¯¯¯
= −
1
2
log
cosh x + 1
cosh x − 1
30.
Z
senh2x dx =
1
4
senh 2x −
1
2
x
31.
Z
cosh2x dx =
1
4
senh 2x +
1
2
x
32.
Z
sech2x dx = tanh x
33.
Z
senh−1 x
a
dx = xsenh−1 x
a
−
p
x2 − a2 (a > 0)
34.
Z
cosh−1 x
a
dx =
½
xcosh−1 x
a −
p
x2 − a2
£
cosh−1
¡
x
a
¢
> 0, a > 0
¤
xcosh−1 x
a +
p
x2 − a2
£
cosh−1
¡
x
a
¢
< 0, a > 0
¤
35.
Z
tanh−1 x
a
dx = xtanh−1 x
a
+
a
2
log
¯¯
a2 − x2
¯¯
36.
Z
1
p
a2 + x2
dx = log
³
x +
p
a2 + x2
´
= sen h−1 x
a
(a > 0)
37.
Z
1
a2 + x2 dx =
1
2
arctan
x
a
(a > 0)
38.
Z p
a2 − x2 dx =
x
2
p
a2 − x2 +
a2
2
arcsen
x
a
(a > 0)
39.
Z ¡
a2 − x2¢3
2 dx =
x
8
¡
5a2 − 2x2¢p
a2 − x2 +
3a4
8
arcsen
x
a
(a > 0)
40.
Z
1
p
a2 − x2
dx = arcsen
x
a
(a > 0)
41.
Z
1
a2 − x2 dx =
1
2a
log
¯¯¯¯
a + x
a − x
¯¯¯¯
230 Tabla de Integrales
42.
Z
1
(a2 − x2)
3
2
dx =
x
a2
p
a2 − x2
43.
Z p
x2 ± a2 dx =
x
2
p
x2 ± a2 ±
a2
2
log
¯¯¯
x +
p
x2 ± a2
¯¯¯
44.
Z
1
p
x2 − a2
dx = log
¯¯ ¯
x
+
p
x2 − a2
¯¯¯
= cosh−1 x
a
(a > 0)
45.
Z
1
x(a + bx)
dx =
1
a
log
¯¯¯¯
x
a + bx
¯¯¯¯
46.
Z
x
p
a + bx dx =
2 (3bx − 2a) (a + bx)
3
2
15b2
47.
Z p
a + bx
x
dx = 2
p
a + bx + a
Z
1
x
p
a + bx
dx
48.
Z
x
p
a + bx
dx =
2 (bx − 2a)
p
a + bx
3b2
49.
Z
1
x
p
a + bx
dx =
8<
:
...