Integrals
1
Table of Standard Integrals 1. Z x n dx = x n+1 n +1 + C (n 6= -1) 2. Z dx x = ln |x| + C 3. Z e x dx = e x + C 5. Z sin x dx = - cos x + C 6. Z cos x dx = sin x + C 7. Z tan x dx = - ln cos x + C 8. Z cot x dx = ln sin x + C 15. Z dx a 2 + x 2 = 1 a tan -1 x a + C 9. Z sec 2 x dx = tan x + C 10. Z cosec 2 x dx = - cot x + C 11. Z sec x dx = ln sec x + tan x + C 12. Z cosecx dx = ln cosecx - cot x + C 13. Z sinh x dx = cosh x + C 14. Z cosh x dx = sinh x + C 17. Z dx √ a 2 - x 2 = sin -1 x a + C (|x| <a) 16. Z dx a 2 - x 2 = 1 2a ln a + x a - x + C 19. Z dx √ x 2 + a 2 = sinh -1 x a + C = ln x + √ x 2 + a 2 + C 0 20. Z dx √ x 2 - a 2 = cosh -1 x a + C = ln x + √ x 2 - a 2 + C 0 (x>a) Linearity: Z ( λf (x)+ μg (x) ) dx = λ Z f (x) dx + μ Z g (x) dx Integration by substitution: Z f (u(x)) du dx dx = Z f (u) du Integration by parts: Z f (x)g 0 (x) dx = f (x)g (x) - Z f 0 (x)g (x) dx 18. Z dx = 1 2a ln + C x - a x + a 4. Z + C ln x x 2 - a 2 a x dx = a x
description
Integrales reglas
Transcript of Integrals
Table of Standard Integrals
1.
∫
xn dx =xn+1
n + 1+ C (n 6= −1)
2.
∫
dx
x= ln |x| + C
3.
∫
ex dx = ex + C
5.∫
sin x dx = − cos x + C
6.∫
cos x dx = sin x + C
7.∫
tan x dx = − ln∣
∣cos x∣
∣ + C
8.∫
cot x dx = ln∣
∣sin x∣
∣ + C
15.∫
dx
a2 + x2=
1
atan−1
(x
a
)
+ C
9.
∫
sec2 x dx = tanx + C
10.
∫
cosec2x dx = − cot x + C
11.
∫
sec x dx = ln∣
∣sec x + tan x∣
∣ + C
12.
∫
cosecx dx = ln∣
∣cosecx − cot x∣
∣ + C
13.
∫
sinh x dx = cosh x + C
14.
∫
cosh x dx = sinh x + C
17.∫
dx√a2 − x2
= sin−1
(x
a
)
+ C (|x| < a)
16.
∫
dx
a2 − x2=
1
2aln
∣
∣
∣
a + x
a − x
∣
∣
∣+ C
19.∫
dx√x2 + a2
= sinh−1
(x
a
)
+ C = ln(
x +√
x2 + a2
)
+ C ′
20.∫
dx√x2 − a2
= cosh−1
(x
a
)
+C = ln(
x+√
x2 − a2
)
+C ′ (x > a)
Linearity:
∫
(
λf(x) + µg(x))
dx = λ
∫
f(x) dx + µ
∫
g(x) dx
Integration by substitution:
∫
f(u(x))du
dxdx =
∫
f(u) du
Integration by parts:
∫
f(x)g′(x) dx = f(x)g(x) −∫
f ′(x)g(x) dx
18.∫
dx=
1
2aln
∣
∣
∣
∣
∣
∣+ C
x − ax + a
4.∫
+ Cln x
x2 − a2
ax dx = ax
El_nahuel_Pa
Línea
El_nahuel_Pa
Nota adhesiva
Marked definida por El_nahuel_Pa
