> 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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Question
![TABLE OF INTEGRALS
Forms Involving a + bu
u du
1
b²
47.
48.
49.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
S
62.
S
S
a bu
50. —++b+c
S
S
S
S
S
S
S
S
a + bu
S
u² du
a + bu
S
du
u(a + bu)
u du
(a + bu)²
u√a + bu du
du
u²(a + bu)
u² du
(a + bu)²
du
u(a + b)²
S
u du
a + bu
V
u² du
du
u√a + bu
a + bu
la + bu
u
√a + bu
u²
2
1
· [(a + bu)² - 4a(a + bu) + 2a² In |a + bu|] + C
263
u" du
a + bu
(a + bu
du
u"√a + bu du
du
u" √a + bu
1
a
1
b3
In
du =
2
36²
a
b²(a + bu)
au
1
1
a(a + bu)
2
156³
1
√a
u
a + bu
a
2
15b²
a
In
-a
a ln |a + bu) + C
bu
2
(3bu
tan
+
V
-1
1
a
-
√a + bu
И
2u" √a + bu
b(2n 1)
(bu − 2a) √√a + bu + C
2
b(2n + 3)
+ C
2
a + bu
a²
a + bu
√a
a + bu + √a
a + bu
2√a + bu + a
In
(8a² + 3b²u²-4abu) √a + bu + C
+
In |a + bu| + C
u
af
2a)(a + bu)³/² + C
√a + bu
a(n − 1)un-1
-
-a
a + bu
b
2
u
S
C
2a ln a
+ C,
du
u√a + bu
2na
b(2n + 1)
+ C
u" (a + bu)³/2
+ C, if a > 0
du
u√a + bu
REFERENCE PAGES
b(2n
3)
2a(n − 1)
bu + C
+1) +
if a < 0
na
n-1
¹ § u²²¹ √a + bu du
du]
un-1 du
√a + bu
du
₁"-¹ √√a + bu
u
8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4366dfe0-8b79-493a-bd35-71195c5ab896%2F3ecbea03-e96f-4588-b4ea-2f6ebaf73144%2F5i70kij_processed.jpeg&w=3840&q=75)
Transcribed Image Text:TABLE OF INTEGRALS
Forms Involving a + bu
u du
1
b²
47.
48.
49.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
S
62.
S
S
a bu
50. —++b+c
S
S
S
S
S
S
S
S
a + bu
S
u² du
a + bu
S
du
u(a + bu)
u du
(a + bu)²
u√a + bu du
du
u²(a + bu)
u² du
(a + bu)²
du
u(a + b)²
S
u du
a + bu
V
u² du
du
u√a + bu
a + bu
la + bu
u
√a + bu
u²
2
1
· [(a + bu)² - 4a(a + bu) + 2a² In |a + bu|] + C
263
u" du
a + bu
(a + bu
du
u"√a + bu du
du
u" √a + bu
1
a
1
b3
In
du =
2
36²
a
b²(a + bu)
au
1
1
a(a + bu)
2
156³
1
√a
u
a + bu
a
2
15b²
a
In
-a
a ln |a + bu) + C
bu
2
(3bu
tan
+
V
-1
1
a
-
√a + bu
И
2u" √a + bu
b(2n 1)
(bu − 2a) √√a + bu + C
2
b(2n + 3)
+ C
2
a + bu
a²
a + bu
√a
a + bu + √a
a + bu
2√a + bu + a
In
(8a² + 3b²u²-4abu) √a + bu + C
+
In |a + bu| + C
u
af
2a)(a + bu)³/² + C
√a + bu
a(n − 1)un-1
-
-a
a + bu
b
2
u
S
C
2a ln a
+ C,
du
u√a + bu
2na
b(2n + 1)
+ C
u" (a + bu)³/2
+ C, if a > 0
du
u√a + bu
REFERENCE PAGES
b(2n
3)
2a(n − 1)
bu + C
+1) +
if a < 0
na
n-1
¹ § u²²¹ √a + bu du
du]
un-1 du
√a + bu
du
₁"-¹ √√a + bu
u
8
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 + x²dx=
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