U deTalca - Matesup - Universidad de Talca

Cálculo
Formulario
Sean u, v funciones de la variable x;
Z
(u ± v) dx =
(1)
Z
(2)
Z
u dx ±
Z
v dx
Z
a u dx = a
u dx
Z
(3)
dx = x + C
Z
(4)
Z
(5)
Z
(6)
xn+1
x dx =
+ C,
n+1
n
dx
x
1
= arctan + C
2
+x
a
a
Z
x + a
dx
1
+ C = 1 tanh−1 x + C
ln (18)
=
2
2
a −x
2a
x − a
a
a
Z
dx
x
= arcsin + C, a > 0
(19) √
2
2
a
a −x
(17)
n 6= −1
(20)
Z
dx
= ln |x| + C
x
(21)
ax
a dx =
+C
ln a
Z
(22)
Z
(24)
Z
tan x dx = − ln | cos x| + C
U
(25)
Z
(10) csc x dx = ln | csc x − cot x| + C
(26)
Z
(13)
2
sec x dx = tan x + C
Z
2
csc x dx = − cot x + C
(14)
Z √
a2
−
x2
x
x√ 2
a2
2
dx =
a − x + arcsin + C
2
2
a
x2 + a2 dx =
√
x√ 2
a2
x + a2 + ln(x + x2 + a2 ) + C
2
2
x2 − a2 dx =
√
x√ 2
a2
x − a2 − ln(x + x2 − a2 ) + C
2
2
sinh x dx = cosh x + C
cosh x dx = sinh x + C
Z
(29)
Z
(30)
sech2 x dx = tanh x + C
cschx2 dx = −ctghx + C
Z
sec x tan x dx = sec x + C
sechx tanh x dx = −secx + C
(31)
Z
(16)
Z √
(28)
Z
(15)
√
Z
cot x dx = ln | sin x| + C
Z
√
dx
= ln(x + x2 − a2 ) + C
x 2 − a2
Z √
(27)
Z
(12)
√
Z
sec x dx = ln | sec x + tan x| + C
(11)
√
dx
x
= ln |x + a2 + x2 | + C = sinh−1 + C
2
2
a
a +x
de
cos x dx = sin x + C
(9)
√
dx
1
x
= arcsec + C
2
2
a
a
x x −a
√
Z
1
a + a2 − x 2
dx
1
|x|
√
(23)
= − ln
+C
+ C = − sech−1
2
2
a
x
a
a
x a −x
x
sin x dx = − cos x + C
(8)
a2
Z
Z
(7)
a y n constantes.
Ta
lca
Z
Derivadas
Z
csc x cot x dx = − csc x + C
Instituto de Matemática y Fı́sica
(32)
cschx coth x dx = −cscx + C
Universidad de Talca