Differentiation/Integration Flashcards
1
Q
Reciprocal Identity
1
cos
A
sec
2
Q
Pythagorean Identity
1+cot^2=
A
csc^2
3
Q
cosacosb+sinasinb
A
cos(a-b)
4
Q
Pythagorean Identity
sec^2
A
1+tan^2=sec^2
5
Q
∫ cscxcotx dx
A
-cscx + C
6
Q
∫secx dx
A
ln Isecx + tanxI + C
7
Q
Pythagorean Identity
sin and cos
A
sin^2+cos^2=1
8
Q
∫ x^n dx
A
x^(n+1) / n+1 (n cannot =-1)
9
Q
sinacosb+cosasinb
A
sin(a+b)
10
Q
∫ e^x dx
A
e^x + C
11
Q
d/dx (lnx)
A
1/x
12
Q
Pythagorean Identity
cot and csc
A
1+cot^2=csc^2
13
Q
Pythagorean Identity
csc^2
A
1+cot^2=csc^2
14
Q
d/dx (cotx)
A
-csc²x
15
Q
∫ 1/x dx
A
ln |x| + C
16
Q
cos(a+b)
A
cosacosb-sinasinb
17
Q
∫ sec²x dx
A
tanx + C
18
Q
sinacosb-cosasinb
A
sin(a-b)
19
Q
∫ secxtanx dx
A
secx + C
20
Q
d/dx (cscx)
A
-cscxcotx
21
Q
d/dx (x^n)
A
nx^n-1
22
Q
Pythagorean Identity
tan and secant
A
1+tan^2=sec^2
23
Q
∫ 1 dx
xlnx
A
ln I lnx I + C
24
Q
n
Σi2
i=1
A
n(n+1)(2n+1)
6
25
Pythagorean Identity
sin^2+cos^2=
1
26
d/dx (sinx)
cosx
27
sin(a+b)
sinacosb+cosasinb
28
d/dx (secx)
secxtanx
29
Reciprocal Identities
Cot
_1_
tan
30
n
Σi
i=1
_n(n+1)_
2
31
∫ xsinx dx
sinx - xcosx + C
32
∫ xex dx
(x-1)ex + C
33
n
Σi3
i=1
_n_2_(n+1)_2
4
34
d/dx (x)
1
35
∫ a dx
ax + C
36
n
Σc
i=1
cn
37
∫ tanx dx
-ln Icos xI + C
38
∫cot2x dx
-cotx - x + C
39
d/dx (ax)
a
40
Reciprocal Identity
csc
_1_
sin
41
d/dx (cosx)
-sinx
42
∫ 1 dx
x + C
43
∫ a^x dx
a^x / lna +c (a\>0, a cannot =1)
44
∫ln x dx
x ln x - x + C
45
∫ xcosx dx
cosx + xsinx + C
46
∫ csc²x dx
-cotx + C
47
∫ sinx dx
-cosx + C
48
∫ cosx dx
sinx + C
49
tan identity
_sin_
cos
50
sin(a-b)
sinacosb-cosasinb
51
cos(a-b)
cosacosb+sinasinb
52
d/dx (e^x)
e^x
53
Reciprocal Identity
_1_
sin
csc
54
_tana+tanb_
1-tanatanb
tan(a+b)
55
tan(a-b)
_tana-tanb_
1+tanatanb
56
Pythagorean Identity
1
sin^2+cos^2=1
57
Reciprocal Identities
sec
_1_
cos
58
Reciprocol Identity
_1_
tan
cot
59
Pythagorean Identity
1+tan^2=
sec^2
60
∫tan2x dx
tanx - x + C
61
∫cscx dx
-ln Icscx + cotxI + C
62
∫cotx dx
ln IsinxI + C
63
d/dx (tanx)
sec²x
64
cosacosb-sinasinb
cos(a+b)
65
tan(a+b)
_tana+tanb_
1-tanatanb
66
cot identity
_cos_
sin
67
∫sin2x dx
_x_ -_sin(2x)_
2 4
68
∫cos2x dx
_x_ + _sin(2x)_ + C
2 4
69
∫ _1_ dx
(a2-x2)½
arcsin _x_ + C
a
70
∫ _1_ dx
a2+x2
_1_ arctan _x_ + C
a a
71
Trigonometric Substitution
(a²-x²)½
x=asinØ
1-sin2Ø=cos2Ø
72
Trigonometric Subistution
(a2+x2)½
x=atanØ
1 + tan2Ø = sec2Ø
73
Trigonometric Substitution
(x2-a2)½
x = asecØ
sec2Ø - 1 = tan2Ø
74
Double Angle Identity
sin2x
2sinxcosx
75
Double Angle Identity
cos2x
cos2x - sin2x
or
1 - 2sin2x
or
2cos2x - 1
76
Double Angle Identity
tan2x
_2tanx_
1 - tan2x
77
Half Angle Identity
sin2x
or
sin _x_
2
_1 - cos2x_
2
78
Half Angle Identity
cos2x
or
cos**_x_**
2
_1 + cos2x_
2
79
Half Angle Identity
tan**_x_**
2
_sinx_
1 + cosx
or
_1 - cosx_
sinx
