1
Q
∫x^n dx
A
1/n+1 X^n+1 +C
2
Q
∫1/x dx
A
ln|x|+C
3
Q
∫1/(ax+b)dx
A
1/a ln|a+b|+C
4
Q
∫lnax dx
A
x(lnax -1)
5
Q
∫a^x dx
A
a^x /lna +C
5
Q
∫e^x dx
A
e^x +c
6
Q
∫cscxdx
A
ln|tanx/2|+C
7
Q
∫csc^2(ax)dx
A
-1/a cot(ax)+C
8
Q
∫sin(ax) dx
A
-1/a cos(ax)+C
8
Q
∫secx *cscx dx
A
ln|tanx|+C
9
Q
∫cos(ax)
A
1/asin(ax)+C
10
Q
∫tan(ax) dx
A
-1/a ln(cos(ax)) +C
11
Q
∫sec^2 (ax) dx
A
1/a tan(ax) +C
12
Q
∫sec(x)tan(x) dx
A
secx +C
13
Q
∫secx dx
A
ln|secx+tanx|+C
14
Q
work
A
(a to b)∫ F(x) dx
15
Q
Force of spring
A
spring constant * distance stretched
16
Q
Force of y
A
mass *gravity
17
Q
what is density * volume
A
mass
18
Q
∫lnx dx
A
x(lnx-1)+C
19
Q
∫du / sqrt(a^2 - u^2)
A
sin^-1 (u/a)+C
19
Q
∫log(base a)x
A
x/lna (lnx-1)+C
20
Q
∫du/ a^2 +u^2
A
1/a tan^-1 (u/a)+C
21
Q
work for water
A
(a to b) ∫densitygravityarea*x
22
∫du/ u(sqrt(u^2 -a^2)
1/a sec^-1(u/a) +C
23
∫udv
uv -∫ vdu +C
24
LIATE
Log , inverse trig, alegriaic, trig, exponential
25
integrating sin+cos products with odd power trig
1. write odd as even power * 1 of it
2.get it in terms of the other
3. integrate making u the higher power
26
integrating sin+cos products with both even powers
1. double angle identities to get into polynomial of cos(2x)
2. apply strategies to things with powers greater than 1
27
double angle cos^2(x)
1/2 (1+cos(2x)
28
double angle for sin^2(x)
1/2 (1-cos(2x))
29
identity for cos^2(x)
1-sin^2(x)
29
identity for sin^2(x)
1-cos^2(x)
30
sin(ax)cos(bx)
1/2 sin((a+b)x +1/2 sin ((a-b)x)
31
cos(ax)cos(bx)
1/2 cos((a+b)x +1/2 cos ((a-b)x)
32
tan is even sec is odd
1. write tan in terms of secx
2. write polynomial in sec
3 reduction method
32
integrating tan+sec products with sec being even
1.split out a sec^2(x) while keeping secx to even power
2.u sub with tan as u
33
integrating sin+cos products with odd power tan
1. split out secxtanx
2 write tan in even power
3. u is secx
34
identity of sec^2(x)
tan^2(x) +1
35
tan reduction formula
tan^n (x) dx
1/n-1 tan^(n-1) (x) - ∫tan^ (n-2) (x)dx
36
sec reduction formula
sec^n (x) dx
1/n-1 sec^(n-2) (x)tan(x) + n-2/(n-1)
∫tan^ (n-2) (x)dx
37
trig sub a^2-x^2
x = asin(theta)
38
trig sub a^2 + x^2
x = atan(theta)
39
trig sub x^2 - a^2
x = a(sec(theta)
