> Use the Table of Integrals to find the following antiderivatives. Be sure to cite the Formula number of the integral in the Tables (eg. #81). dx x²-4 √√√1 + x² dx =
> Use the Table of Integrals to find the following antiderivatives. Be sure to cite the Formula number of the integral in the Tables (eg. #81). dx x²-4 √√√1 + x² dx =
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...
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![> Use the Table of Integrals to find the following antiderivatives. Be sure to cite the Formula number
of the integral in the Tables (eg. #81).
dx
x²-4
√√1 + x² dx=
Find f xdx
x+1
by first dividing.
Do your results agree?
xdx
x+1]
Then use Formula #47 to find ſ-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8df10466-bb36-424d-be07-c1f915d82bc7%2Ff7128231-aad3-4156-ab23-77beadae57b1%2F4dignf8_processed.png&w=3840&q=75)
Transcribed Image Text:> Use the Table of Integrals to find the following antiderivatives. Be sure to cite the Formula number
of the integral in the Tables (eg. #81).
dx
x²-4
√√1 + x² dx=
Find f xdx
x+1
by first dividing.
Do your results agree?
xdx
x+1]
Then use Formula #47 to find ſ-
![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%2F8df10466-bb36-424d-be07-c1f915d82bc7%2Ff7128231-aad3-4156-ab23-77beadae57b1%2Fmag3r2q_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
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