Inte
Tabla de Integrales
(PUEDE SUMARSE UNA CONSTANTE ARBITRARIA A CADA INTEGRAL)
1
xn+1
n+1
1.
xn dx =
2.
1
dx = log | x |
x
3.
ex dx = ex
4.
ax dx =
5.
sen x dx = − cos x
6.
cos x dx = sen x
7.
tan x dx = − log |cos x|
8.
cot x dx = log |sen x|
9.
sec x dx = log |sec x + tan x| = log tan
(n = −1)
ax
log a
227
1
1x+ π
2
4
228
Tabla de Integrales
1
x
2
10.
csc x dx = log |csc x − cot x| = log tan
11.
arcsen
x
x √2
dx = x arcsen
+ a − x2
a
a
12.
arccos
x
x√
dx = x arccos − a2 − x2
a
a
13.
arctan
x
xa
dx = x arctan − log a2 + x2
a
a2
14.
sen2 mx dx =
1
(mx − sen mx cos mx)
2m
15.
cos2 mx dx =
1
(mx + sen mx cos mx)
2m
16.sec2 x dx = tan x
17.
csc2 x dx = −cot x
18.
senn x dx = −
19.
cosn x dx =
cosn−1 x sen x n − 1
+
n
n
20.
tann x dx =
tann−1 x
−
n−1
tann−2 x dx
21.
cotn x dx =
cotn−1 x
−
n−1
cotn−2 x dx
22.
secn x dx =
tan x secn−2 x n − 2
+
n−1
n−1
23.
cot x csc n−1 x n − 2
csc x dx =
+
n−2
n−1
24.
senh x dx = cosh x
25.
cosh xdx = senh x
senn−1 x cos x n − 1
+
n
n
n
(a > 0)
(a > 0)
(a > 0)
senn−2 x dx
cosn−2 x dx
(n = 1)
(n = 1)
secn−2 x dx
cscn−2 x dx
(n = 1)
(n = 1)
229
26.
tanh x dx = log |cosh x|
27.
coth x dx = log |sen hx|
28.
sech x dx = arctan (senh x)
29.
csch x dx = log tanh
30.
1
1
senh2 x dx = senh 2x − x
4
2
31.
1
1
cosh2 x dx = senh2x + x
4
2
32.
sech2 x dx = tanh x
33.
senh−1
34.
x
x√
dx = xsenh−1 − x2 − a2 (a > 0)
a
a
√
xcosh−1 x − √x2 − a2 cosh−1
−1 x
a
cosh
dx =
xcosh−1 x + x2 − a2 cosh−1
a
a
35.
tanh−1
36.
√
37.
38.
39.
40.
41.
x
1
cosh x + 1
= − log
2
2
cosh x − 1
√
1
1
x
dx = arctan
2
+x
2
a
a2 − x2 dx =
a2 − x2
√
3
2
x
x√ 2
a2a − x2 + arcsen
2
2
a
dx =
(a > 0)
(a > 0)
(a > 0)
√
x
x
3a4
5a2 − 2x2
arcsen
a 2 − x2 +
8
8
a
1
x
dx = arcsen
a
a2 − x2
a2
> 0, a > 0
< 0, a > 0
x
xa
dx = xtanh−1 + log a2 − x2
a
a2
√
x
1
dx = log x + a2 + x2 = sen h−1
a
a2 + x2
a2
x
a
x
a
a+x
1
1
dx =
log
2
−x
2a
a−x
(a > 0)
(a > 0)
230
42.
43.
Tabla deIntegrales
1
(a2 − x2 )
√
x2
±
a2
3
2
dx =
a2
√
x
a2 − x2
√
x√ 2
a2
2±
dx =
x ±a
log x + x2 ± a2
2
2
√
x
1
dx = log x + x2 − a2 = cosh−1
a
x2 − a 2
44.
√
45.
x
1
1
dx = log
x(a + bx)
a
a + bx
46.
47.
48.
49.
(a > 0)
3
√
2 (3bx − 2a) (a + bx) 2
x a + bx dx =
15b2
√
√
1
a + bx
√
dx = 2 a + bx + a
dx
x
xa + bx
√
x
2 (bx − 2a) a + bx
√
dx =
3b2
a + bx
√
√
1
√ log √a+bx−√a (a > 0)
1
a
a+bx+ a
√
dx =
√2 arctan a+bx (a > 0)
x a + bx
−a
−a
√
50.
51.
52.
53.
√
1
x a2 − x2 dx = − a2 − x2
3
√
a2 − x2
x
3
2
√
√
x
a4
x
x2 a2 − x2 dx =
2x2 − a2
a2 − x2 + arcsen
8
8
a
√
a + a 2 − x2
1
1
√
dx = − log
a
x
x a2 − x2
54.
√
55.
√56.
√
a2 − x2
a+
dx = a2 − x2 − a log
x
√
x
dx = − a2 − x2
a2 − x2
x2
x√ 2
x
a2
dx = −
(a > 0)
a − x2 + arcsen
2 − x2
2
2
a
a
√
√
√
a + x2 + a2
x2 + a2
dx = x2 + a2 − a log
x
x
(a > 0)
231
√
57.
58.
59.
60.
61.
√
√
x2 − a 2
a
x
dx = x2 − a2 − a arccos
= x2 − a2 − arcsec
x
|x|
a
√
12
x x2 ± a2 dx =
x ± a2
3
x
√
1
x2
+a2
dx =
x
1
√
log
a
a + x2 + a2
1
√
63.
1
dx =
2 + bx + c
ax
65.
66.
67.
(a > 0)
√
x
dx = x2 ± a2
x2 ± a 2
62.
64.
3
2
1
a
dx = arccos
a
|x|
x x2 − a 2
√
1
x2 ± a2
√
dx = ±
a2 x
x2 x2 ± a2
√
(a > 0)
√
b− 2
√1
log 2ax+b+√b2 −4ac
b2 −4ac
2ax+
b −4ac
2
√2
√ ax+b
arctan 4ac−b2
4ac−b2
(b2 > 4ac)
(b2 < 4ac)...
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