cal 2 Flashcards
(27 cards)
1
Q
∫ cf(x) dx =?
A
c∫ f(x)dx
2
Q
∫ (f(x) +/- g(x)) dx =?
A
∫ f(x)dx +/- ∫ g(x)dx
3
Q
∫ x^n dx =?
A
(1/(n+1) )(x^(n+1)) +C
4
Q
∫ 1/x dx =?
A
ln|x|+C
5
Q
∫e^x dx = ?
A
e^x +C
6
Q
∫b^x dx =?
A
1/lnb (b^x) +C
7
Q
∫cosx dx =?
A
sinx +C
8
Q
∫sinx dx =?
A
-cosx +C
9
Q
∫sec^2x dx =?
A
tanx +C
10
Q
∫csc^2x dx =?
A
-cotx +C
11
Q
∫secxtanx dx =?
A
secx +C
12
Q
∫cscxcotx dx =?
A
-cscx +C
13
Q
∫1/(√1-x^2)dx =?
A
arcsinx +C
14
Q
∫1/(1+x^2)dx =?
A
arctanx +C
15
Q
∫tanx dx =?
A
- ln |cosx| +C = ln |secx| +C
16
Q
∫cotx dx =?
A
ln |sinx| +C
17
Q
∫secx dx =?
A
ln |secx+tanx| +C
18
Q
∫cscx dx =?
A
ln |cscx-cotx| +C
19
Q
what is the substitution rule?
∫ f(g(x))g’(x)dx =?
A
∫ f(u) du
20
Q
∫lnx dx =?
A
xlnx -x +C
21
Q
∫(ax+b)^n dx =?
A
(1/a)((ax+b)^n+1)/(n+1) +C if n≠ -1
(1/a) ln|ax+b| +C if n= -1
22
Q
∫e^(ax+b) dx =?
A
(1/a)e^(ax+b) +C
23
Q
∫sin(ax+b) dx =?
A
(-1/a)cos(ax+b) +C
24
Q
∫cos(ax+b) dx =?
A
(1/a)sin(ax+b) +C
25
∫sec^2(ax+b) dx =?
(tan(ax+b))/a +C
26
∫dx/(x^2+a^2) =?
(1/a)arctan(x/a) +C
27
∫dx/(√a^2-x^2) =?
arcsin(x/a) +C a>0
