EXAM 1 Flashcards
(36 cards)
1
Q
S a dx
A
ax + C
2
Q
S x^n dx
A
x^n+1 / n+1
3
Q
S (1/x) dx
A
ln |x| + c
4
Q
S e^x dx
A
s^x + c
5
Q
S a^x dx
A
a^x / ln(a) + c
6
Q
S ln(x) dx
A
xln(x) - x + c
7
Q
S cos(x) dx
A
sin(x) + c
8
Q
S sin(x) dx
A
-cos(x) + c
9
Q
S sec^2(x) dx
A
tan(x) + c
10
Q
(ln(x))’
A
1/x
11
Q
(e^x)’
A
e^x
12
Q
a^x =
A
e^(x*ln(a))
13
Q
logb(x) =
A
ln(x) / ln(b)
14
Q
(arcsinx)’
A
1 / sqrt(1-x^2)
15
Q
(arccosx)’
A
-1 / sqrt(1-x^2)
16
Q
(arctanx)’
A
1 / 1 + x^2
17
Q
(arcsec)’
A
1 / |x| sqrt(x^2-1)
18
Q
(arccsc)’
A
-1 / |x| sqrt(x^2-1)
19
Q
(arccot)’
A
-1 / 1+x^2
20
Q
Integration by parts formula
A
S u dv = uv-Svdu
21
Q
Functions hardest to easiest
A
LIATE (log, inverse, algebraic, trig, exponential)
22
Q
S csc^2 dx
A
-cot(x) + c
23
Q
S sec(x)tan(x) dx
A
sec(x) + c
24
Q
S csc(x)cot(x) dx
A
-csc(x) + x
25
S tan(x) dx
ln |sec(x)| + c
26
S cot(x) dx
ln |sin(x)| +c
27
S sec(x) dx
ln |sec(x)+tan(x)| + c
28
S csc(x) dx
ln |csc(x) - cot(x)| + c
29
S sin^2(x) dx
S 1-cos(2x) / 2 dx
30
S cos^2(x) dx
S 1+cos(2x) / 2
31
1 - sin^2 u =
cos^2(u)
32
1 + tan^2 u =
sec^2(u)
33
sec^2 u - 1 =
tan^2(u)
34
sqrt(a^2-x^2) , x =
asin(u)
35
sqrt(a^2 + x^2), x =
atan(u)
36
sqrt(x^2-a^2), x =
asec(u)
