Ch 5 Identities Flashcards
(44 cards)
0
Q
∫du
A
u+C
1
Q
∫kf(u)du
A
K∫f(u)du
2
Q
∫du/u or ∫1/u(du)
A
Ln|u|+C
3
Q
∫[f(u)+/-g(u)]du
A
∫f(u) +/- ∫g(u)
4
Q
∫u^n du
A
(U^n+1)/n+1
5
Q
∫e^udu
A
e^u + C
6
Q
∫a^udu
A
(1/lna)a^u + C
7
Q
∫sinudu
A
-cosu + C
8
Q
∫cosudu
A
Sinu + C
9
Q
∫tanudu
A
-ln |cosu| + C
10
Q
∫cotudu
A
Ln|sinu| + C
11
Q
∫secudu
A
ln |secu +tanu| + C
12
Q
∫cscudu
A
-ln |cscu +cotu| + C
13
Q
∫sec^2udu
A
Tanu + C
14
Q
∫csc^2udu
A
-cotu + C
15
Q
∫secutanudu
A
Secu + C
16
Q
∫cscucotudu
A
-cscu + C
17
Q
d/dx(cu)
A
cu`
18
Q
d/dx(sinu)
A
(Cosu)u`
19
Q
d/dx(cosu)
A
-(Sinu)u`
20
Q
d/dx(tanu)
A
(Sec^2u)u`
21
Q
d/dx(cotu)
A
-(Csc^2u)u`
22
Q
d/dx(secu)
A
(Secutanu)u`
23
Q
d/dx(cscu)
A
-(Cscucotu)u`
24
d/dx(u +/- v)
u` +/- v`
25
d/dx(uv)
uv`+vu`
26
d/dx(u/v)
uv` - vu`/ v^2
27
d/dx(c)
0
28
d/dx(u^n)
nu^n-1(u`)
29
d/dx(x)
1
30
d/dx(|u|)
(u/|u|)(u`)
31
d/dx(lnu)
u`/u
32
d/dx(e^u)
e^u(u`)
33
d/dx(loga u)
u`/(u)(lna)
34
d/dx(a^u)
(a^u)(lna)(u`)
35
d/dx(arcsinu)
u'/√1-u^2
36
d/dx(arccosu)
-u'/√1-u^2
37
d/dx(arctanu)
u`/1+u^2
38
d/dx(arccotu)
-u`/1+u^2
39
d/dx(arcsecu)
u'/|u|√[(u^2)-1]
40
d/dx(arccscu)
-u'/|u|√[(u^2)-1]
41
∫du/√[(a^2)-(u^2)] or ∫1/√[(a^2)-(u^2)] (du)
arcsin(u/a) + C
42
∫du/(a^2)-(u^2)
(1/a)arctan(u/a) + C
43
∫du/u√[(u^2)-(a^2)]
(1/a)arcsec(|u|/a) + C
