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
Exponential and Logarithmic Forms
1
96.
Su
uleau du = (au 1)ea" + C
a²
97. Su
1 = = = = 1²eª² - 1²/² √ 1₁²-¹1 - du
eª
98.
S
ea sin bu du =
q² + b²
eau
99.
Se
eau cos bu du
a² + b²
Hyperbolic Forms
103.
S
sinh u du = cosh u + C
104.
S
cosh u du = sinh a + C
105.
S
tanh u du = In cosh u + C
106.
S coth u du = In | sinh u|+ C
S sech u du = tan"'|sinh u|+ C
107.
Forms Involving √2au-u², a>0
113.
S
√2au- u² du =
u-a
2
114.
Su
u√√2au-u² du
=
2u²-au-3a²
6
√2au u²
115.
du = √√√2au- u²+ a cos-¹
u
√2au-u²
2√2au-u2
116.
du =
- cos-1
11
du
117.
=cos-¹
a-u
a
+ C
118.
-√2au- u²+ a cos-¹
(u + 3a)
119.
√2au-u²+
2
2au-u²
120.
+ C
au
uneau du =
S
S
√2au
u du
√√2au-u²
u² du
√2au-u²
du
u√√2au-u2
S
S
=
u²
=
REFERENCE PAGE
(a sin bu b cos bu) + C
(a cos bu + b sin bu) + C
¹ (₁ = ") ₁
a
q²
√2au-u²+ cos-¹
√2au-u²+
a-u
a
a-u
a
au
¹(ª = ²) +
a
+ C
+ C
3a²
COS-1
2
+ C
a³
- ²ª cos-¹(ª = ¹) +
+ C
a-u
a
100.
101.
102.
+ C
In u du = u ln u - u + C
4²+1
u" In u du =
(n + 1)²
du
In | In u + C
u In u
S
esch u du = In | tanhju|+C
| sech’u du = tanh u + C
csch'u du = −coth u + C
sech u tanh u du = -sech u + C
S
S
csch u coth u du = −csch u + C
finu
S
S
108.
109.
110.
111.
112.
+ C
-[(n+1) Inu 1] + C](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad29c243-17bc-495f-9a75-f51d725c2e92%2F81ed54ae-1d3e-460f-8f3f-eef519dcc952%2Fpbpqxd8_processed.png&w=3840&q=75)
Transcribed Image Text:TABLE OF INTEGRALS
Exponential and Logarithmic Forms
1
96.
Su
uleau du = (au 1)ea" + C
a²
97. Su
1 = = = = 1²eª² - 1²/² √ 1₁²-¹1 - du
eª
98.
S
ea sin bu du =
q² + b²
eau
99.
Se
eau cos bu du
a² + b²
Hyperbolic Forms
103.
S
sinh u du = cosh u + C
104.
S
cosh u du = sinh a + C
105.
S
tanh u du = In cosh u + C
106.
S coth u du = In | sinh u|+ C
S sech u du = tan"'|sinh u|+ C
107.
Forms Involving √2au-u², a>0
113.
S
√2au- u² du =
u-a
2
114.
Su
u√√2au-u² du
=
2u²-au-3a²
6
√2au u²
115.
du = √√√2au- u²+ a cos-¹
u
√2au-u²
2√2au-u2
116.
du =
- cos-1
11
du
117.
=cos-¹
a-u
a
+ C
118.
-√2au- u²+ a cos-¹
(u + 3a)
119.
√2au-u²+
2
2au-u²
120.
+ C
au
uneau du =
S
S
√2au
u du
√√2au-u²
u² du
√2au-u²
du
u√√2au-u2
S
S
=
u²
=
REFERENCE PAGE
(a sin bu b cos bu) + C
(a cos bu + b sin bu) + C
¹ (₁ = ") ₁
a
q²
√2au-u²+ cos-¹
√2au-u²+
a-u
a
a-u
a
au
¹(ª = ²) +
a
+ C
+ C
3a²
COS-1
2
+ C
a³
- ²ª cos-¹(ª = ¹) +
+ C
a-u
a
100.
101.
102.
+ C
In u du = u ln u - u + C
4²+1
u" In u du =
(n + 1)²
du
In | In u + C
u In u
S
esch u du = In | tanhju|+C
| sech’u du = tanh u + C
csch'u du = −coth u + C
sech u tanh u du = -sech u + C
S
S
csch u coth u du = −csch u + C
finu
S
S
108.
109.
110.
111.
112.
+ C
-[(n+1) Inu 1] + C
Transcribed Image Text:1. Use the Table of Integrals to evaluate the integral. Show ALL work. ²³ 11x³ √√4x² – x¹ dx
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