+C +C +C |+C | sec u + tan u + C In |csc u - cot u + C -"-¹ sin^-³u du n "=¹ cos¹u du n tan*-²u du +C u²+ C =u²) + C u√1-u² 4 +C -1 - = 7 [cot'u du cotu- cot 76. n 17. secu du = 78. feserud n-1 n-1 79. sin au sin bu dusin (a − b)u__sin (a + b)u 2(a - b) 2(a + b) 80. cos au cos budu - +1=²5₁ sec-²u du - cot u ese-³u + 1 = ² fese" u du 81. sin au cos bu du = 92. fu -tan u sec-²u+ 94. 82. u sin u du = sin u - u cos u + C 83. fu 33. fuª sin™¹ 84. 14. fuª sin u du = −uª cos u +1 cos u du = cos u+ u sin u + C 85. fu* cos u du = u² sin u-n fu²- 86. sinºu cos u du = sin (a - b)usin (a + b)u + 2(a - b) 2(a + b) cos (a - b)u 2(a - b) sin"'u du = ·fuª cos-¹u du = +nfuric du n+1 sin u du sin"-lu cosu n-1 n+m n+m sin cosu n+m + + u tan-'u du = "²+¹ tan-¹ - + C cos (a + b)u 2(a + b) u du + C m +C du "R+T [~ ² T [1² sin²¹ - S - T - - +1 +C sinu com n+msin'u cogn- u** du [+] ¹ cos'¹u + S₁ n7
+C +C +C |+C | sec u + tan u + C In |csc u - cot u + C -"-¹ sin^-³u du n "=¹ cos¹u du n tan*-²u du +C u²+ C =u²) + C u√1-u² 4 +C -1 - = 7 [cot'u du cotu- cot 76. n 17. secu du = 78. feserud n-1 n-1 79. sin au sin bu dusin (a − b)u__sin (a + b)u 2(a - b) 2(a + b) 80. cos au cos budu - +1=²5₁ sec-²u du - cot u ese-³u + 1 = ² fese" u du 81. sin au cos bu du = 92. fu -tan u sec-²u+ 94. 82. u sin u du = sin u - u cos u + C 83. fu 33. fuª sin™¹ 84. 14. fuª sin u du = −uª cos u +1 cos u du = cos u+ u sin u + C 85. fu* cos u du = u² sin u-n fu²- 86. sinºu cos u du = sin (a - b)usin (a + b)u + 2(a - b) 2(a + b) cos (a - b)u 2(a - b) sin"'u du = ·fuª cos-¹u du = +nfuric du n+1 sin u du sin"-lu cosu n-1 n+m n+m sin cosu n+m + + u tan-'u du = "²+¹ tan-¹ - + C cos (a + b)u 2(a + b) u du + C m +C du "R+T [~ ² T [1² sin²¹ - S - T - - +1 +C sinu com n+msin'u cogn- u** du [+] ¹ cos'¹u + S₁ n7
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![TABLE OF INTEGRALS
Trigonometric Forms
63. sin²u du-u-sin 2u + C
64. cos²u du =u+sin 2u + C
65. tan²u du = tan u - u + C
Scot'u du = −cot u - u + C
67. · sin³u du = − 4(2 + sin³u) cos u + C
68.
[ cos'u du = (2+ cos²u) sin u + C
66.
69. tan'u dutan²u + In | cos u + C
S
70.
Scot'u du = −cot²u - In [sin u + C
71.
1.5 sec¹u du = sec u tan u + ¼ In sec u + tan u + C
² So
csc³u du-esc u cot u +In |csc u - cot u + C
"sin"-²u du
+ ₁ = 1 Sc cos"-2u du
n
72
iss
73.
sin u du =
74.
1. f cos'u du = — cosª
75. tan u du =
90.
91.
S.
·S₁
sin-¹ cos u +
Inverse Trigonometric Forms
87. sin u du = u sin-¹u + √I-u²+ C
u sin-¹ u du =
1
n-1
88. cos'u du = u cosu - √1 − u² + C
89.
ftan
tan u du = u tan¹u-In(1 + ²) + C
u cos'u du
slu sin
=
tanu
u+
u - Sti
tan"-²u du
2u²-1
4
2u²
4
sin u +
cos lu
u√√1-u²
4
-u²
4
+ C
+ C
76. f cot'u du
171. ↑ sectu du =
78.
3. fcsc²u du =
79.
80.
81.
83.
=
-1
n-1
95.
-1
n-1
92. f u tan-
cos (a b)u
2(a - b)
82. u sin u du = sin u - u cos u + C
S₁
I
cotu- fcot-u du
sin au sin bu du = sin (a − b)u_sin (a + b)u + C
2(a - b)
2(a + b)
cos au cos bu dusin (a - b)usin (a + b)u
2(a - b)
sin au cos bu du =
86. sin'u cosu du
fsi
S
84.
·S u" sin u du = -u" cos u + n
tan'u du
-tan u sec-¹u+
93.
3. f uª sin¯'u du =
=
cos u du = cos u + u sin u + C
-cot u esc-¹u+
34. f * con²¹ d =
u du
utan u du
85.
5. § uª cos u du = uª sin u − n § u*¯¹ sin u du
sin"-¹u cos+u
n-1
n+msin-¹u cosu du
n+msin"u cosm-u du
n-
+"=² sec-¹u du
n-
cosu+nfu-
u²+1
2
+1=² fese-³u du
n-
sin cosu
n+m
•~ +1 [~~
1
n+ 1
n+m
1
n+1
[
-tan-¹u-/+C
+ C
2(a + b)
cos (a + b)u
2(a + b)
u+1 sinu
cos u du
+
+
[² ²³ + f
u+tanu
du
u²
+ C
+1 du
4*+1
du
--[²4]
1+ u²
n-1
n-1
n-1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4366dfe0-8b79-493a-bd35-71195c5ab896%2F7b6a26cd-02c3-4c70-8b51-95faf7f569ab%2Focpgss_processed.png&w=3840&q=75)
Transcribed Image Text:TABLE OF INTEGRALS
Trigonometric Forms
63. sin²u du-u-sin 2u + C
64. cos²u du =u+sin 2u + C
65. tan²u du = tan u - u + C
Scot'u du = −cot u - u + C
67. · sin³u du = − 4(2 + sin³u) cos u + C
68.
[ cos'u du = (2+ cos²u) sin u + C
66.
69. tan'u dutan²u + In | cos u + C
S
70.
Scot'u du = −cot²u - In [sin u + C
71.
1.5 sec¹u du = sec u tan u + ¼ In sec u + tan u + C
² So
csc³u du-esc u cot u +In |csc u - cot u + C
"sin"-²u du
+ ₁ = 1 Sc cos"-2u du
n
72
iss
73.
sin u du =
74.
1. f cos'u du = — cosª
75. tan u du =
90.
91.
S.
·S₁
sin-¹ cos u +
Inverse Trigonometric Forms
87. sin u du = u sin-¹u + √I-u²+ C
u sin-¹ u du =
1
n-1
88. cos'u du = u cosu - √1 − u² + C
89.
ftan
tan u du = u tan¹u-In(1 + ²) + C
u cos'u du
slu sin
=
tanu
u+
u - Sti
tan"-²u du
2u²-1
4
2u²
4
sin u +
cos lu
u√√1-u²
4
-u²
4
+ C
+ C
76. f cot'u du
171. ↑ sectu du =
78.
3. fcsc²u du =
79.
80.
81.
83.
=
-1
n-1
95.
-1
n-1
92. f u tan-
cos (a b)u
2(a - b)
82. u sin u du = sin u - u cos u + C
S₁
I
cotu- fcot-u du
sin au sin bu du = sin (a − b)u_sin (a + b)u + C
2(a - b)
2(a + b)
cos au cos bu dusin (a - b)usin (a + b)u
2(a - b)
sin au cos bu du =
86. sin'u cosu du
fsi
S
84.
·S u" sin u du = -u" cos u + n
tan'u du
-tan u sec-¹u+
93.
3. f uª sin¯'u du =
=
cos u du = cos u + u sin u + C
-cot u esc-¹u+
34. f * con²¹ d =
u du
utan u du
85.
5. § uª cos u du = uª sin u − n § u*¯¹ sin u du
sin"-¹u cos+u
n-1
n+msin-¹u cosu du
n+msin"u cosm-u du
n-
+"=² sec-¹u du
n-
cosu+nfu-
u²+1
2
+1=² fese-³u du
n-
sin cosu
n+m
•~ +1 [~~
1
n+ 1
n+m
1
n+1
[
-tan-¹u-/+C
+ C
2(a + b)
cos (a + b)u
2(a + b)
u+1 sinu
cos u du
+
+
[² ²³ + f
u+tanu
du
u²
+ C
+1 du
4*+1
du
--[²4]
1+ u²
n-1
n-1
n-1
Transcribed Image Text:MATH 152 Reading Assignment
Read this section briefly. Then answer the following questions.
▸ Using integration techniques, show that the antiderivative [sin³ xdx is -cosx+C.
§5.8 Stewart
cos³x
3
Write down the result of Formula #67 in the Table of Integrals in the back of your book for sin³ xdx.
sin xda
How can you reconcile the book's result with the one you got above?
Now use Formula #73 in the book to find [sin³ xdx.
|sin xda =
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning