common
derivatives
nx
(x]
(x
ax
=
nut
=
+
Cn +1
n 1
+
=
integrals
Ssinxdx
ScosXdx
=
Inkx) + c
SexdX ex+ C
sinx + c
=
Ssec2xdX
Stdx
-cosx + C
=
=
tanx + C
=
SsecX +anx
=
Scs2dx
secX + C
=
- cgX + C
ScscxctgxdX
=
-
csCX + C
Sax = arctan(
S
= arcsecant
Stanxax
=
JSx
dx
=
-du
=
u
=
u
=
coSX
al = = SinX
-
-Inlt a
In 1csx* + C
In/csX1" + C
=
du = sinx
(cosx)"
= JeX
=
x
mod I
review
R summation
11
,
f(x)
=
x+
2x(8 3
,
n-subintervals
Formulas
·
kn(n + 1)
al
2
N
3-0=
=
k2
n(n + 1) (2n 1
+
=
6
Xk
ROX
=
=
K
.
(2) =
3)
f(x)
=
x + 2x
< [f(x)4X
=
(zx 2(zk)
=
+
=
akt
5/
&
(Int(n)
&
n
+ ) + q(n+ 1)
9 (nti)(2n
2n
a
Yen2 + 27n + 9
2n2
n
+
n
-
/2
Im
- +9
=
96
99
·
out
30
2)
U-Sub.
S*cod
u
du
=
=
Sin x
wsXdX
①
=
)dWarctan()
(*xarctaC
3/2
③ go back to Y
=
arctan(u)
Min
O
#
=
arctanlsn/
tansman(in-tan(s)
tan- (sin)
=
formula
3
S'(x
y
-
-31dx
=
f (x) f m))f(x) ))
+
-
+
=
+)
+
j m))ax
+
axi
x-axis
11
3
-3)
-)(,
x
S"
js) j"x ja
+
.
x
+
3
a
+
-
-
-
- 3x)
+
!
- 3 -( 3m)
+
+
=
2
1=
2 +
X
go back to
5.
ax
e
u
du-in-in-mi) (i)
-
2
①
Set-In( )
u = X+ 1
u
-
du
+
1= X
=
1 +0
=
1
Gu
=
x+ 1
u= X + 1
"gia sect gaa
IttanX
au
=
o+
sectX
-
0
1
=
=
u = 0+ 1
u = 1+ 1
a
not
back to x
lit
② change your
limits
①
u =
+
go
=
1
= 2
-
In (2)
-
1
displacement
①
distance
and
②
i
>
direction
·
.
displacement
0
vit
=
sinit)
(I . ]
sint) -cost 1 -2)
=
+
② distance
S
sintsinta
int
cos()
=
E
at
#
T
i
-cost]] ast
-
sint
=
+
0
N
-
wsH
-
sint
t
=
=
-
(S)
( -) +
o
0
,
i
,
2
2
-
()
-
1 - Cs(π)
=
+
T
(
(
+
till 270
2 +m
+
1
=
2
FTC
[F(x)
f(x) - F(X)
g
+ (x)dx -
F(b)
Part 1
A(x)
=
S*f(t)at
(A((]
=
+(x)
=
-
F(a)
=
+
(iint a.
In/sinx)
-
1
In (sinx)
#
I
=
sec X
COS
*
I
sin
*
5 Find
tan
#'(x)
get Nedt
-
it
=
F(x)
fexi at
1 + (e)
-
-
Setanxfe
=
1 +
ex
.
an e
x
=
tanx
u=
du sechX
=
secx
11 sinx)
-
d
zex
:
&x
cos X