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TABLA INTEGRALES
∫
1
∫
3
∫
6
∫
xm dx =
af (x) dx = a
∫
11
∫
14
∫
17
∫
20
∫
23
∫
26
∫
29
∫
32
∫
33
∫
35
∫
36
∫
38
f (x) dx,
ex dx = ex ,
si
∫
m ̸= −1
dx
= ln(x), x > 0
∫ x
∫
f (y) dy
7
f (y) dx =
dy/dx
4
UTP, Pereira
∫
f m+1 (x)
2
f m (x)f ′ (x) dx =
m+1
∫ ′
f (x) dx
5
= ln[f (x)], f (x) > 0
f (x)
∫
8
x
∫
0 dx = c
af (x)
a>0
10 af (x) f ′ (x) dx =
ln(a)
∫
∫
sen(x) dx = − cos(x),
12
cos(x) dx = sen(x),
13 tan(x) dx = − ln[cos(x)]
∫
∫
cot(x) dx = ln[sen(x)],
15 df (x) = f (x),
16
sec(x) dx = ln | sec(x) + tan(x)|
∫
∫
sec2 (x) dx = tan(x),
18
sec(x) tan(x) dx = sec(x),
19
sec2 [f (x)]f ′ (x) dx = tan[f (x)]
∫
∫
csc2 (x) dx = − cot(x),
21
ln(x) dx = x ln (x) − x
22
csc(x) dx = − ln | csc (x) + cot (x) |
∫
∫
x − sen(x) cos(x)
sen2 (x) dx =
24
csc(x) cot(x) dx = − csc(x) 25 tan2 (x) dx = tan(x) − x
2
∫
∫
( )
√
x + sin (x) cos (x)
dx
1
dx
−1 x
2 + x2 √
cos2 (x) dx =
27
=
tan
,
28
=
ln
+
a
x
2
2
2
a
a
a2 + x2
∫ a +x
∫
(x)
√
dx
dx
1
dx
x
−
a
2 − a2 √
√
= sen−1
=
ln
+
x
,
30
=
ln
31
x
2 − a2
a
x2 − a2
2a [ x + a a2 − x2
x(
)]
[
(
)]
√
√
√
1
x
1
x
a2 − x2 dx =
x a2 − x2 + a2 sen−1
=
x a2 − x2 + a2 arctan √
2
a∫
2
a2 − x2
∫
(x)
n−1
cos
(ax) sen(ax) n − 1
dx
1
√
cosn (ax) dx =
+
cosn−2 (ax) dx
34
= sec−1
na
n
a
a
x x2 − a2
∫
senn−1 (ax) cos(ax) n − 1
n
n−2
sen (ax) dx = −
+
sen
(ax) dx
na ∫
n
∫
tann−1 (ax)
eax
tann (ax) dx =
− tann−2 (ax) dx
37 eax cos(bx) dx = 2
[a cos(bx) + b sen(bx)]
a(n − 1)
a + b2
ax
e
eax sen(bx) dx = 2
[a sen(bx) − b cos(bx)]
NOTA: Agregar la respectiva constante de integración
a + b2
ax dx =
9
xm+1
,
m +∫1
Por: Fernando Valdés M ©,
a
,
ln(a)
si
TRIGONOMETRÍA CIRCULAR
5
6
sen2 (x) + cos2 (x) = 1
sen(x + π/2) = cos(x)
cos(x + π/2) = sen(x)
2 tan(x)
tan(2x) =
1 − tan2 (x)
sen(−x) = − sen(x),
csc(x) = 1/ sen(x),
7
tan(x) =
8
a sen(x) + b cos(x) = R sen(x + α)
9
a sen(x) + b cos(x) = R cos(x − α)
10
sen−1 (x) + cos−1 (x) = π/2
1
2
3
4
1 + tan2 (x) = sec2 (x)
sin(π − x) = sen(x),
sen(2x) = 2 sen(x) cos(x)
1 − cos(2x)
sen2 (x) =
2
cos(−x) = cos(x)
sec(x) = 1/ cos(x)
sen(x)
cos(x)
cos(x)
cot(x) =
sen(x)
√
R = a2 + b2 =⇒
√
R = a2 + b2
=⇒
=⇒
=⇒
tan−1 (x) + cot−1 (x) = π/2
1
1 + cot2 (x) = csc2 (x)
sen(π/2 − x) = cos(x)
cos(2x) = cos2 (x) − sen2 (x)
1 + cos(2x)
cos2 (x) =
2
tan(−x) = − tan(x)
cot(x) = 1/ tan(x)
b
a a
tan(α) =
b
tan−1 (x) + tan−1 (1/x) = π/2
tan(α) =
TRIGONOMETRÍA HIPERBÓLICA
3
ex + e−x
2
cosh2 (x) − senh2 (x) = 1
√
senh−1 (x) = ln(x + x2 + 1)
4
senh2 (x) =
1
2
cosh(x) =
−1 + cosh(2x)
2
ex − e−x
2
1 − tanh2 (x) = sech2 (x)
√
cosh−1 (x) = ln(x + x2 − 1)
senh(x) =
cosh2 (x) =
1 + cosh(2x)
2
2
senh(x)
cosh(x)
coth2 (x) − 1 = csch2 (x)
(
)
1
1+x
tanh−1 (x) = ln
2
1−x
tanh(x) =
cosh(2x) = cosh2 (x) + senh2 (x)