R E F E R E N C E PA G E 1
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ALGEBRA
GEOMETRY
Arithmetic Operations
Geometric Formulas
a
c
ad # bc
# !
b
d
bd
a
b
a
d
ad
! ! !
c
b
c
bc
d
a!b # c" ! ab # ac
a#c
a
c
! #
b
b
b
Formulas for area A, circumference C, and volume V:
Triangle
Circle
Sector of Circle
A ! 12 bh
A ! "r 2
A ! 12 r 2%
C ! 2" r
s ! r % !% in radians"
! 12 ab sin %
a
Exponents and Radicals
m
x
! x m$ n
xn
1
x$ n ! n
x
x m x n ! x m#n
!x " ! x
m n
mn
#$
n
x 1'n ! s
x
n
n
x m'n ! s
x m ! (s
x )m
A ! 4" r 2
&
n
!
s
¨
r
Sphere
V ! 43 " r 3
n
n
n
xy ! s
xs
y
s
n
r
b
xn
yn
x
y
!xy"n ! x n y n
r
h
¨
Cylinder
V ! " r 2h
Cone
V ! 13 " r 2h
A ! " rsr 2 # h 2
n
x
x
s
! n
y
sy
r
r
h
h
Factoring Special Polynomials
r
x 2 $ y 2 ! !x # y"!x $ y"
x 3 # y 3 ! !x # y"!x 2 $ xy # y 2"
x 3 $ y 3 ! !x $ y"!x 2 # xy # y 2"
Distance and Midpoint Formulas
Binomial Theorem
!x # y"2 ! x 2 # 2xy # y 2
!x $ y"2 ! x 2 $ 2xy # y 2
Distance between P1!x1, y1" and P2!x 2, y2":
d ! s!x 2 $ x1"2 # ! y2 $ y1"2
!x # y"3 ! x 3 # 3x 2 y # 3xy 2 # y 3
!x $ y"3 ! x 3 $ 3x 2 y # 3xy 2 $ y 3
!x # y"n ! x n # nx n$ 1y #
# ))) #
#$
n!n $ 1" n$ 2 2
x y
2
#$
n n$ k k
x y # ) ) ) # nxy n$ 1 # y n
k
n
n!n $ 1" ) ) ) !n $ k # 1"
where
!
k
1 ! 2 ! 3 ! ))) ! k
Midpoint of P1 P2 :
x1 # x 2 y1 # y2
,
2
2
Slope of line through P1!x1, y1" and P2!x 2, y2":
m!
$ b ( sb 2 $ 4ac
.
2a
$
Lines
Quadratic Formula
If ax 2 # bx # c ! 0, then x !
#
y2 $ y1
x 2 $ x1
Point-slope equation of line through P1!x1, y1" with slope m:
Inequalities and Absolute Value
y $ y1 ! m!x $ x1"
If a & b and b & c, then a & c.
If a & b, then a # c & b # c.
Slope-intercept equation of line with slope m and y-intercept b:
If a & b and c ' 0, then ca & cb.
y ! mx # b
If a & b and c & 0, then ca ' cb.
If a ' 0, then
% x % ! a means x ! a or x ! $ a
% x % & a means $ a & x & a
% x % ' a means x ' a or x & $ a
Circles
Equation of the circle with center !h, k" and radius r:
!x $ h"2 # ! y $ k"2 ! r 2
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
R E F E R E N C E PA G E 2
TRIGONOMETRY
Angle Measurement
Fundamental Identities
! radians ! 180"
csc # !
1
sin #
sec # !
1
cos #
tan # !
sin #
cos #
cot # !
cos #
sin #
"# in radians#
cot # !
1
tan #
sin 2# $ cos 2# ! 1
Right Angle Trigonometry
1 $ tan 2# ! sec 2#
1 $ cot 2# ! csc 2#
sin"% ## ! % sin #
cos"% ## ! cos #
tan"% ## ! % tan #
sin
1" !
!
rad
180
1 rad !
180"
!
¨
r
s ! r#
sin # !
cos # !
opp
hyp
csc # !
adj
hyp
sec # !
opp
tan # !
adj
s
r
hyp
opp
hyp
hyp
adj
opp
¨
adj
$ %
adj
cot # !
opp
cos
Trigonometric Functions
sin # !
y
r
csc # !
r
y
cos # !
x
r
sec # !
r
x
tan # !
y
x
cot # !
x
y
r
1
π
¨
a
C
The Law of Cosines
x
b
a 2 ! b 2 $ c 2 % 2bc cos A
b 2 ! a 2 $ c 2 % 2ac cos B
y
y=tan x
Addition and Subtraction Formulas
2π
π
x
_1
2π x
A
c 2 ! a 2 $ b 2 % 2ab cos C
1
_1
B
sin A
sin B
sin C
!
!
a
b
c
(x, y)
y=cos x
2π
!
% # ! cot #
2
c
y
y=sin x
tan
!
% # ! cos #
2
The Law of Sines
y
Graphs of Trigonometric Functions
y
!
% # ! sin #
2
$ %
$ %
π
x
sin"x $ y# ! sin x cos y $ cos x sin y
sin"x % y# ! sin x cos y % cos x sin y
cos"x $ y# ! cos x cos y % sin x sin y
y
y=csc x
y
y
y=cot x
cos"x % y# ! cos x cos y $ sin x sin y
1
1
_1
y=sec x
π
2π x
π
_1
2π x
π
2π x
tan"x $ y# !
tan x $ tan y
1 % tan x tan y
tan"x % y# !
tan x % tan y
1 $ tan x tan y
Double-Angle Formulas
sin 2x ! 2 sin x cos x
Trigonometric Functions of Important Angles
cos 2x ! cos 2x % sin 2x ! 2 cos 2x % 1 ! 1 % 2 sin 2x
#
radians
sin #
cos #
tan #
0"
30"
45"
60"
90"
0
!!6
!!4
!!3
!!2
0
1!2
s2!2
s3!2
1
1
s3!2
s2!2
1!2
0
0
s3!3
1
s3
—
tan 2x !
2 tan x
1 % tan2x
Half-Angle Formulas
sin 2x !
1 % cos 2x
2
cos 2x !
1 $ cos 2x
2
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
R E F E R E N C E PA G E 3
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SPECIAL FUNCTIONS
f !x" ! x a
Power Functions
(i) f !x" ! x n , n a positive integer
y
y
y=x$
y=x^
y=≈
(_1, 1)
y=x%
(1, 1)
x
0
(_1, _1)
x
0
(1, 1)
y=x#
n even
n odd
n
(ii) f !x" ! x 1#n ! s
x , n a positive integer
y
y
(1, 1)
0
(1, 1)
x
0
x
ƒ=œ„
(iii) f !x" ! x !1 !
1
x
x
ƒ=#œx„
y
y=∆
1
0
1
y
Inverse Trigonometric Functions
arcsin x ! sin!1x ! y &? sin y ! x and !
x
"
"
$ y$
2
2
π
2
lim tan!1 x ! !
0
x
arccos x ! cos!1x ! y &? cos y ! x and 0 $ y $ "
arctan x ! tan!1x ! y &? tan y ! x and !
"
"
# y#
2
2
_ π2
x l !%
lim tan!1 x !
xl%
"
2
y=tan–!x=arctan x
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
"
2
R E F E R E N C E PA G E 4
SPECIAL FUNCTIONS
y
Exponential and Logarithmic Functions
log a x ! y
&?
ln x ! log e x,
y=´
y
a !x
y=x
ln e ! 1
where
1
ln x ! y &? e y ! x
y=ln x
0
Cancellation Equations
Laws of Logarithms
loga#a x $ ! x
a log a x ! x
1. log a# xy$ ! log a x " log a y
ln# e x $ ! x
e ln x ! x
2. loga
!"
x
y
! loga x ! loga y
lim e x ! 0
” 4 ’®
1
1
y
10® 4®
e®
lim e x ! $
x l !$
3. loga# x r $ ! r loga x
” 2 ’®
xl$
lim ln x ! !$
lim ln x ! $
x l 0"
2®
x
1
xl$
y
y=log™ x
1.5®
y=ln x
y=log∞ x
y=log¡¸ x
1
1®
0
x
1
x
0
Exponential functions
Logarithmic functions
Hyperbolic Functions
sinh x !
e x ! e!x
2
csch x !
1
sinh x
cosh x !
e x " e!x
2
sech x !
1
cosh x
tanh x !
sinh x
cosh x
coth x !
cosh x
sinh x
y=cosh x
y
y=tanh x
x
y=sinh x
Inverse Hyperbolic Functions
y ! sinh!1x
y ! cosh!1x &? cosh y ! x
y ! tanh!1x
sinh!1x ! ln( x " sx 2 " 1 )
&? sinh y ! x
&?
tanh y ! x
and
y#0
cosh!1x ! ln( x " sx 2 ! 1 )
tanh!1x ! 12 ln
! "
1"x
1!x
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
R E F E R E N C E PA G E 5
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D I F F E R E N T I AT I O N R U L E S
General Formulas
1.
d
!c" ! 0
dx
2.
d
& cf !x"' ! c f #!x"
dx
3.
d
& f !x" " t!x"' ! f #!x" " t#!x"
dx
4.
d
& f !x" ! t!x"' ! f #!x" ! t#!x"
dx
5.
d
& f !x" t!x"' ! f !x" t#!x" " t!x" f #!x" (Product Rule)
dx
6.
d
dx
7.
d
f ! t!x"" ! f #! t!x"" t#!x" (Chain Rule)
dx
8.
d
!x n " ! nx n!1 (Power Rule)
dx
$ %
f !x"
t!x"
!
t!x" f #!x" ! f !x" t#!x"
& t!x"' 2
(Quotient Rule)
Exponential and Logarithmic Functions
9.
d
!e x " ! e x
dx
10.
d
!a x " ! a x ln a
dx
11.
d
1
ln x !
dx
x
12.
d
1
!log a x" !
dx
x ln a
# #
Trigonometric Functions
13.
d
!sin x" ! cos x
dx
14.
d
!cos x" ! !sin x
dx
15.
d
!tan x" ! sec 2x
dx
16.
d
!csc x" ! !csc x cot x
dx
17.
d
!sec x" ! sec x tan x
dx
18.
d
!cot x" ! !csc 2x
dx
Inverse Trigonometric Functions
19.
d
1
!sin!1x" !
dx
s1 ! x 2
20.
d
1
!cos!1x" ! !
dx
s1 ! x 2
21.
d
1
!tan!1x" !
dx
1 " x2
22.
1
d
!csc!1x" ! !
dx
x sx 2 ! 1
23.
1
d
!sec!1x" !
dx
x sx 2 ! 1
24.
d
1
!cot!1x" ! !
dx
1 " x2
Hyperbolic Functions
25.
d
!sinh x" ! cosh x
dx
26.
d
!cosh x" ! sinh x
dx
27.
d
!tanh x" ! sech 2x
dx
28.
d
!csch x" ! !csch x coth x
dx
29.
d
!sech x" ! !sech x tanh x
dx
30.
d
!coth x" ! !csch 2x
dx
Inverse Hyperbolic Functions
31.
d
1
!sinh!1x" !
dx
s1 " x 2
32.
d
1
!cosh!1x" !
dx
sx 2 ! 1
33.
d
1
!tanh!1x" !
dx
1 ! x2
34.
d
1
!csch!1x" ! !
dx
x sx 2 " 1
35.
d
1
!sech!1x" ! !
dx
x s1 ! x 2
36.
d
1
!coth!1x" !
dx
1 ! x2
# #
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
R E F E R E N C E PA G E 6
TA B L E O F I N T E G R A L S
Basic Forms
1.
y u dv ! uv " y v du
2.
y u du ! n ! 1 ! C, n " "1
3.
y u ! ln % u % ! C
4.
y e du ! e ! C
5.
y
6.
y csc u cot u du ! "csc u ! C
12. y tan u du ! ln % sec u % ! C
13. y cot u du ! ln % sin u % ! C
14. y sec u du ! ln % sec u ! tan u % ! C
11.
u n!1
n
du
u
u
a u du !
15.
au
!C
ln a
y sin u du ! "cos u ! C
7.
y cos u du ! sin u ! C
8.
y sec u du ! tan u ! C
9.
y
10.
y sec u tan u du ! sec u ! C
16.
y sa " u ! sin a ! C, a # 0
17.
y a ! u ! a tan a ! C
18.
y u su " a ! a sec a ! C
19.
y a " u ! 2a ln u " a ! C
20.
y u " a ! 2a ln u ! a ! C
2
csc2u du ! "cot u ! C
y csc u du ! ln % csc u " cot u % ! C
du
"1
2
du
2
1
"1
u
2
1
du
2
"1
u
2
du
2
1
2
du
2
u
2
1
2
$
$
u!a
u"a
$
$
Forms Involving sa 2 ! u 2 , a # 0
21.
y sa ! u du ! 2 sa ! u ! 2 ln(u ! sa ! u ) ! C
22.
y u sa ! u du ! 8 !a ! 2u " sa ! u " 8 ln(u ! sa ! u ) ! C
23.
y
a ! sa 2 ! u 2
sa 2 ! u 2
du ! sa 2 ! u 2 " a ln
u
u
24.
y
sa 2 ! u 2
sa 2 ! u 2
du ! "
! ln(u ! sa 2 ! u 2 ) ! C
u2
u
25.
y sa ! u ! ln(u ! sa ! u ) ! C
26.
y sa ! u ! 2 sa ! u " 2 ln(u ! sa ! u ) ! C
27.
y u sa ! u ! " a ln
28.
y u sa ! u ! "
29.
y !a ! u "
2
u
2
2
2
2
u
2
a2
2
2
2
2
2
2
a4
2
2
$
du
2
2
2
u
2
2
2
2
du
1
2
2
du
2
2
du
2
!C
2
u 2 du
2
$
2
2 3#2
!
$
a2
sa 2 ! u 2 ! a
u
2
$
2
!C
sa 2 ! u 2
!C
a 2u
u
a 2 sa 2 ! u 2
!C
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
R E F E R E N C E PA G E 7
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TA B L E O F I N T E G R A L S
Forms Involving sa 2 ! u 2 , a # 0
30.
y sa ! u du ! 2 sa ! u " 2 sin a " C
31.
y u sa ! u du ! 8 !2u ! a " sa ! u " 8 sin a " C
32.
y
a " sa 2 ! u 2
sa 2 ! u 2
du ! sa 2 ! u 2 ! a ln
u
u
33.
y
1
u
sa 2 ! u 2
du ! ! sa 2 ! u 2 ! sin!1 " C
u2
u
a
34.
y sa ! u ! ! 2 sa ! u " 2 sin a " C
35.
y u sa ! u ! ! a ln
36.
y u sa ! u ! ! a u sa ! u " C
37.
y !a ! u " du ! ! 8 !2u ! 5a "sa ! u " 8 sin a " C
38.
y !a ! u " ! a sa ! u " C
2
2
u
2
2
2
u
2
a2
2
2
!1
2
2
u
a4
2
!1
%
u 2 du
2
u
2
!1
"C
u
2
du
%
1
2
2
du
2
a2
2
%
u
1
2
2
2
2
2
u
2 3#2
du
2
a " sa 2 ! u 2
u
%
"C
2
2
2
2
3a 4
2
!1
u
u
2 3#2
2
2
2
Forms Involving su 2 ! a 2 , a # 0
39.
y su ! a du ! 2 su ! a ! 2 ln $ u " su ! a $ " C
40.
y u su ! a du ! 8 !2u ! a " su ! a ! 8 ln $ u " su ! a $ " C
41.
y
a
su 2 ! a 2
du ! su 2 ! a 2 ! a cos!1
"C
u
u
42.
y
su ! a
su ! a
du ! !
" ln u " su 2 ! a 2 " C
u2
u
43.
y su ! a ! ln $ u " su ! a $ " C
44.
y su ! a ! 2 su ! a " 2 ln $ u " su ! a $ " C
45.
y u su ! a !
46.
y !u ! a " ! ! a su ! a " C
2
2
u
2
2
2
u
2
a2
2
2
2
2
2
2
2
a4
2
2
$ $
2
2
2
du
2
2
2
u
2
2
2
a2
2
2
2
du
2
2
su 2 ! a 2
"C
a 2u
du
2
$
2
u 2 du
2
$
2
u
2 3#2
2
2
2
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
R E F E R E N C E PA G E 8
TA B L E O F I N T E G R A L S
Forms Involving a ! bu
47.
y a ! bu ! b (a ! bu " a ln ) a ! bu )) ! C
48.
y a ! bu ! 2b [!a ! bu" " 4a!a ! bu" ! 2a ln ) a ! bu )] ! C
49.
y u!a ! bu" ! a ln a ! bu ! C
50.
y u !a ! bu" ! " au ! a ln
51.
y !a ! bu" ! b !a ! bu" ! b ln ) a ! bu ) ! C
52.
y u!a ! bu" ! a!a ! bu" " a ln
53.
y !a ! bu" ! b
54.
y u sa ! bu du ! 15b !3bu " 2a"!a ! bu" ! C
55.
y sa ! bu ! 3b !bu " 2a" sa ! bu ! C
56.
y sa ! bu ! 15b !8a ! 3b u " 4abu" sa ! bu ! C
57.
y u sa ! bu ! sa ln sa ! bu ! sa ! C, if a $ 0
u du
1
2
u 2 du
1
2
2
3
du
'
1
du
'
u
1
'
b
2
2
u du
a
2
2
du
1
1
2
2
(
1
2
a ! bu "
3
!C
1
2
u 2 du
'
a ! bu
u
'
'
a ! bu
u
!C
a2
" 2a ln a ! bu
a ! bu
)
2
*
) !C
3$2
2
u du
2
2
u 2 du
2
2
2
2
3
du
'
1
!
2
s"a
sa ! bu " sa
&
tan"1
'
a ! bu
! C,
"a
if a # 0
58.
y
sa ! bu
du ! 2 sa ! bu ! a
u
59.
y
b
sa ! bu
sa ! bu
du ! "
!
u2
u
2
60.
y u sa ! bu du ! b!2n ! 3" u !a ! bu" " na y u
61.
y sa ! bu ! b!2n ! 1" " b!2n ! 1" y sa ! bu
62.
y u sa ! bu ! " a!n " 1"u
u n du
du
n
#
2
n
2u nsa ! bu
y u sa ! bu
du
y u sa ! bu
du
n
3$2
2na
sa ! bu
n"1
"
n"1
%
sa ! bu du
u n"1 du
b!2n " 3"
2a!n " 1"
y u sa ! bu
du
n"1
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
R E F E R E N C E PA G E 9
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TA B L E O F I N T E G R A L S
Trigonometric Forms
63.
y sin u du ! u ! sin 2u " C
76.
64.
y cos u du ! u " sin 2u " C
y cot u du ! n ! 1 cot u ! y cot u du
77.
65.
y tan u du ! tan u ! u " C
y sec u du ! n ! 1 tan u sec u " n ! 1 y sec u du
66.
y cot u du ! !cot u ! u " C
78.
y csc u du ! n ! 1 cot u csc u " n ! 1 y csc u du
79.
y sin au sin bu du ! 2!a ! b" ! 2!a " b" " C
y cos au cos bu du ! 2!a ! b" " 2!a " b" " C
1
2
2
1
4
1
2
2
1
4
2
2
!1
n
n!1
n!2
1
n
!1
n
n!2
n!2
n!2
n!2
n!2
sin!a ! b"u
n!2
sin!a " b"u
67.
y sin u du ! ! !2 " sin u" cos u " C
68.
y cos u du ! !2 " cos u" sin u " C
80.
69.
y tan u du ! tan u " ln # cos u # " C
81.
y sin au cos bu du ! ! 2!a ! b" ! 2!a " b" " C
70.
y cot u du ! ! cot u ! ln # sin u # " C
82.
y u sin u du ! sin u ! u cos u " C
71.
y sec u du ! sec u tan u " ln # sec u " tan u # " C
83.
y u cos u du ! cos u " u sin u " C
72.
y csc u du ! ! csc u cot u " ln # csc u ! cot u # " C
84.
73.
y sin u du ! ! n sin u cos u "
y sin u du
y u sin u du ! !u cos u " n y u
85.
y u cos u du ! u sin u ! n y u
74.
y cos u du ! n cos u sin u "
y cos u du
86.
y sin u cos u du ! !
75.
y tan u du ! n ! 1 tan u ! y tan u du
1
3
3
2
1
3
3
2
1
2
3
2
1
2
3
2
1
2
3
1
2
1
2
3
1
2
1
n
1
n
n!1
n!1
1
n
n!1
n
n!1
n
n!1
n!2
n!2
sin!a ! b"u
sin!a " b"u
cos!a ! b"u
n
n
n
n
n
m
n!2
!
cos!a " b"u
n!1
n!1
cos u du
sin u du
sin n!1u cos m"1u
n!1
"
n"m
n"m
m!1
sin n"1u cos m!1u
"
n"m
n"m
y sin u cos u du
n!2
m
y sin u cos u du
n
m!2
Inverse Trigonometric Forms
87.
y sin u du ! u sin u " s1 ! u " C
88.
y cos u du ! u cos u ! s1 ! u " C
!1
!1
!1
2
!1
y tan u du ! u tan u ! ln!1 " u " " C
90.
y
91.
y u cos u du !
!1
1
2
93.
y u sin u du ! n " 1 u
94.
y u cos u du ! n " 1 u
95.
y u tan u du ! n " 1 u
!1
n
!1
u2 " 1
u
tan!1u ! " C
2
2
1
$
n"1
sin!1u !
2
2u 2 ! 1
u s1 ! u 2
u sin u du !
sin!1u "
"C
4
4
!1
!1
y u tan u du !
2
89.
!1
92.
2u 2 ! 1
u s1 ! u 2
cos!1u !
"C
4
4
n
n
!1
!1
1
1
$
$
n"1
n"1
%
y s1 ! u , n " !1
u n"1 du
2
%
cos!1u "
y s1 ! u , n " !1
tan!1u !
y 1 " u , n " !1
u n"1 du
2
u n"1 du
2
%
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
R E F E R E N C E PA G E 1 0
TA B L E O F I N T E G R A L S
Exponential and Logarithmic Forms
96.
y ue du ! a !au ! 1"e " C
100.
y ln u du ! u ln u ! u " C
97.
y u e du ! a u e ! a y u e du
101.
y u ln u du ! !n " 1" &!n " 1" ln u ! 1' " C
98.
y e sin bu du ! a " b !a sin bu ! b cos bu" " C
102.
y u ln u du ! ln % ln u % " C
99.
y e cos bu du ! a " b !a cos bu " b sin bu" " C
1
au
au
2
1
n au
n
n au
n!1 au
e au
au
2
2
u n"1
n
2
1
e au
au
2
2
Hyperbolic Forms
y sinh u du ! cosh u " C
104. y cosh u du ! sinh u " C
105. y tanh u du ! ln cosh u " C
106. y coth u du ! ln % sinh u % " C
107. y sech u du ! tan % sinh u % " C
y csch u du ! ln % tanh u % " C
109. y sech u du ! tanh u " C
110. y csch u du ! !coth u " C
111. y sech u tanh u du ! !sech u " C
112. y csch u coth u du ! !csch u " C
103.
2
2
!1
Forms Involving s2au ! u 2 , a # 0
# $
113.
y s2au ! u du !
114.
y u s2au ! u du !
115.
y
a!u
s2au ! u 2
du ! s2au ! u 2 " a cos!1
u
a
116.
y
2 s2au ! u 2
a!u
s2au ! u 2
du ! !
! cos!1
u2
u
a
117.
y s2au ! u ! cos
118.
y s2au ! u ! !s2au ! u " a cos
119.
y s2au ! u ! !
120.
y u s2au ! u ! !
2
u!a
a2
a!u
cos!1
s2au ! u 2 "
2
2
a
du
# $
!1
2
u du
a!u
a
# $
# $
2
2
du
2
# $
"C
"C
"C
"C
2
u 2 du
"C
2u 2 ! au ! 3a 2
a3
a!u
cos!1
s2au ! u 2 "
6
2
a
2
1
2
108.
# $
!1
a!u
a
"C
# $
!u " 3a"
3a 2
a!u
cos!1
s2au ! u 2 "
2
2
a
"C
s2au ! u 2
"C
au
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.