Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 12E
Related questions
Question
100%
Find the following indefinite
![b2\a + bu
a\a + bu
a + bu
Set bu + cu?²
Integration Tables
Forms Involving u"
un+1
2. du = In|u|
1.
u" du =
+ C, n + -1
+ C
n + 1
Forms Involving a + bu
4. Sadu - + lala + bul) + c
u
1
3.
a + bu
du =
- a Inla + bu|) + C
(a + bu)?
-1
L(n – 2)(a + bu)*-2' (n -
и
FC
du =
5.
(a + bu)"
+ C, n + 1, 2
1)(a + bu)"-1
u?
du =
6.
a + bu
(2a- bu) + a² In|a + bu + C
u?
a?
du =
7.
(a + bu)?
- 2a Inja + bul) + C
bu -
a + bu
u?
2a
a?
8.
(a + bu)
+ Inla + bu|| + C
du =
bLa + bu
2(a + bu)?
u?
-1
2a
a?
9.
(a + bu)
bL(n - 3)(a + bu)" -3
(п - 2)(а + bu)"-2
(n
- 1)(a + bu)n-1
+ C, n+ 1, 2, 3
+ C
LInla+ bul
1
1
1
du =
|ula + bu)
1
+
a
и
u
+ C
bu
11.
du =
u(a + bu)?
10.
la +
a
1[ a + 2bu
a²[u(a + bu)
1
1
2b
u
12.
du =
u(a + bu)
In
a Ja + bu
+ C
13.
du = -.
+ C
+
In
a\u
u?(a + bu)?
la
a
Forms Involving a + bu + cu?, b? + 4ac
2cu + b
+ C,
V4ac – b2
arctan
b2 < 4ac
1
4ac – b²
14.
du =
|2cu + b - vb2 - 4ac
In
|2cu + b + Jb? – 4acl
1
+ C,
b2 > 4ac
22-4ac
1
du
a + bu + cu?
u
15.
а + bu + cu?
-Inla + bu + cu²| – b
du =
Forms Involving Ja + bu
Sur va+ bu du =
2
u"(a + bu)/2 – na u-Va+ bu du
16.
b(2n + 3)L
1
Va + bu – Ja
+ C, a > 0
In
Ja"I Ja + bu + Ja
1
17,
du =
a + bu
+ C, a < 0
arctan
-a
-a
(2n - 3)b
+
1
- 1
Ja + bu
18.
un-1 Ja + bu
n + 1
du =
u" Ja + bu
a(n - 1)
A3
A4
Appendix B
Integration Tables
1
Ja + bu
du =
2 Ja + bu + a
du
u Ja + bu
19.
u
(a + bu)3/2
un-1
Ja + bu
du =
(2n - 5)b
Va + bu
A gairio an
- 1
du , n + 1
20.
a(n – 1)|
2
un-i
u"
- 2(2a – bu)
3b2
a + bu + C
-
21.
du =
Va + bu
u"-1
= du
Va + bu
u"
2
u"Ja + bu - na
+ tilo i mo
du
(2n + 1)b
22.
Ja + bu
Forms Involving a? ± u?, a > 0
inf
1
du =
arctan
a
1
u
+ C
23.
a2 + u?
a
u -
1
du = -
+ C
24.
du =
u? – a²
a?
u +
1
1
1
25.
(a?
2a (n - 1)(a² + u?)"-1
+ (2n - 3)
(a? + u?)n-1
du
n + 1
Forms Involving Ju? + a', a > 0
a² In\u + Ju* ± a*) + c
26.
u Ju? ± a² du =
u(2u? = a*) /u? ± a² – a* In|u + Ju ± a*]] + c
27.
(ad
/u² + a²
du 3D
Ju + a²
Ja + Ju? + a?
+ C
28.
- a In
Ju|
+ C
29.
du = Ju? - a? - a arcsec
а
grieleval zuo
u² ± a²
u? ± a?
u?
Inļu
du =
+ C
30.
1
du = Inu + /
+ Ju? ± a + C
31.
%3D
Ju? + a²
a +
2 + at
1
arcsec
a
Jul
+ C
32.
du =
+ C
33.
du =
a
Jut ± a') + C
u?
34.
+t
Ju² ± a²
u² ± a²
+ C
a?u
1
1
36.
(u² ± a²)³/2
du = T-
35.
u? Ju? + a²
du =
a2.
+ C
Forms Involving Ja? – u?, a > 0
37. a- du = (-7+d soia) + c
- u? + a? arcsin
u? Ja? – u² du =
a?) Ja? - u? + at arcsin
+ C
38.
A5
Appendix B
Integration Tables
la + Ja? - u?
Va? - u?
du =
39.
du = Ja? - u? - al
+ C 40.
arcsin
a
+ C
u2
1
42. S =+
41.
du = arcsin
+ C
1
+ C
Ja? - u?
du =
uJa?
u?
a²-u?
a?u
1
du =
Va? – u?
43.
-u/a? - u? + a? arcsin
+ C
44.
du =
+ C
u2.
1
du =
a? Ja? - u
45.
(a? - u²)3/2
+ C
Forms Involving sin u or cos u
46.
sin u du = - cos u + C
47.
cos u du = sin u + C
48.
sin? u du =
- sin u cos u) + C
49.
cos? u du =
+ sin u cos u) + C
sin"-1 u cos u
cos" -1 u sin u
n -
50.
sin" u du =
sin"-2 u du
51.
cos" u du =
cos"-2 u du
52.
u sin u du == sin u - u cos u + C
53.
u cos u du = cos u + u sin u + C
54.
sin u du = - u" cos u + nu"-1 cos u du
55.
u" cos u du = u" sin u -
un-1 sin u du
56.
du = tan u sec u + C
57.
du = - cot u + csc + C
1 + sin u
1+ cos u
58.
du =
In tan u| + C
sin u cos u
Forms Involving tan u, cot u, sec u, or csc u
59.
tan u du = - In]cos u| + C
60.
cot u du = In sin u + C
itoH nt
61.
sec u du =
In/sec u + tan u + C
62.
csc u du = In|csc u – cot u +C or
csc u du =
- In|csc u + cot u + C
63.
tan? u du = -u + tan u + C
64.
cot? u du = -u - cot u + C
65.
sec2 u du = tan u + C
66.
csc? u du = - cot u + C
tan"-1
68.
cot"-1u
67.
tan"-2 u du, n # 1
cot" u du =
cot"-2 u du, n # 1
tan" u du =
n - 1
n - 1
secn-2
1
n -
+
n -
69.
u tan u
sec"-2 u du, n + 1
sec" u du =
csch-2
u cot u
csc"-2 u du, n# 1
70.
csc" u du =
A6
Appendix B Integration Tables
+ In/cos u ± sin u|) + C
7 In|sin u ± cos ul) +
72.
du =
1+ tan u
du =
1+ cot u
71.
1
du = u + cot u + csc u + C
74.
du = u - tan u + sec u + C
73.
1+ sec u
1+ csc u
Forms Involving Inverse Trigonometric Functions
Vī - u² + C
75.
arcsin u du = u arcsin u + /1 - u? + C
76.
arccos u du = u arccos u -
arctan u du = u arctan u - In/1 + u? + C
arccot u du = u arccot u + In/1 + u2 + C
77.
78.
In|u +
+ Ju? – 1| + C
Inu + Ju? – 1| + c
79.
arcsec u du = u arcsec u -
80.
arccsc u du = u arccsc u +
Forms Involving e"
e" du = e" + C
82.
ue" du = (u - 1)e" + C
du = u - In(1 + e") + C
1 + elu
83.
u"e" du = u"e" - n
u" - 'e" du
84.
85.
eau sin bu du =
(a sin bu - b cos bu) + C
86.
ea" cos bu du =
(a cos bu + b sin bu) + C
a? + b?
a2 + b2
Forms Involving In u
In u du = u(-1 + In u) + C
u In u du =
u?
-1+2 In u) + C
87.
88.
89.
u" In u du =
nt uzl-1+ (n + 1)In u] + C, n+ -1
So
Sa
90.
(In u)? du = u[2 - 2 In u + (In u)²] + C
91.
(In u)" du = u(In u)" – n
(In u)"- du
Forms Involving Hyperbolic Functions
92.
cosh u du = sinh u + C
93.
sinh u du = cosh u + C
94.
sech? u du = tanh u + C
95.
csch? u du = - coth u + C
sech u tanh u du = - sech u + C
csch u coth u du = - csch u + C
96.
97.
Forms Involving Inverse Hyperbolic Functions (in logarithmic form)
du
du
In(u + Ju? ± a) + C
99.
a? - u?
la +
In
2a
%3D
98.
Ju ± a²
+ C
la -
a + Ja? ± u²
+ C
du
100.
lul
a
UJa² ±
CamScanner](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97c4b753-4d37-4f67-8dde-749f0b47db81%2F12d6a38b-efa6-4722-87dd-fb41b39280ff%2F44z33a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:b2\a + bu
a\a + bu
a + bu
Set bu + cu?²
Integration Tables
Forms Involving u"
un+1
2. du = In|u|
1.
u" du =
+ C, n + -1
+ C
n + 1
Forms Involving a + bu
4. Sadu - + lala + bul) + c
u
1
3.
a + bu
du =
- a Inla + bu|) + C
(a + bu)?
-1
L(n – 2)(a + bu)*-2' (n -
и
FC
du =
5.
(a + bu)"
+ C, n + 1, 2
1)(a + bu)"-1
u?
du =
6.
a + bu
(2a- bu) + a² In|a + bu + C
u?
a?
du =
7.
(a + bu)?
- 2a Inja + bul) + C
bu -
a + bu
u?
2a
a?
8.
(a + bu)
+ Inla + bu|| + C
du =
bLa + bu
2(a + bu)?
u?
-1
2a
a?
9.
(a + bu)
bL(n - 3)(a + bu)" -3
(п - 2)(а + bu)"-2
(n
- 1)(a + bu)n-1
+ C, n+ 1, 2, 3
+ C
LInla+ bul
1
1
1
du =
|ula + bu)
1
+
a
и
u
+ C
bu
11.
du =
u(a + bu)?
10.
la +
a
1[ a + 2bu
a²[u(a + bu)
1
1
2b
u
12.
du =
u(a + bu)
In
a Ja + bu
+ C
13.
du = -.
+ C
+
In
a\u
u?(a + bu)?
la
a
Forms Involving a + bu + cu?, b? + 4ac
2cu + b
+ C,
V4ac – b2
arctan
b2 < 4ac
1
4ac – b²
14.
du =
|2cu + b - vb2 - 4ac
In
|2cu + b + Jb? – 4acl
1
+ C,
b2 > 4ac
22-4ac
1
du
a + bu + cu?
u
15.
а + bu + cu?
-Inla + bu + cu²| – b
du =
Forms Involving Ja + bu
Sur va+ bu du =
2
u"(a + bu)/2 – na u-Va+ bu du
16.
b(2n + 3)L
1
Va + bu – Ja
+ C, a > 0
In
Ja"I Ja + bu + Ja
1
17,
du =
a + bu
+ C, a < 0
arctan
-a
-a
(2n - 3)b
+
1
- 1
Ja + bu
18.
un-1 Ja + bu
n + 1
du =
u" Ja + bu
a(n - 1)
A3
A4
Appendix B
Integration Tables
1
Ja + bu
du =
2 Ja + bu + a
du
u Ja + bu
19.
u
(a + bu)3/2
un-1
Ja + bu
du =
(2n - 5)b
Va + bu
A gairio an
- 1
du , n + 1
20.
a(n – 1)|
2
un-i
u"
- 2(2a – bu)
3b2
a + bu + C
-
21.
du =
Va + bu
u"-1
= du
Va + bu
u"
2
u"Ja + bu - na
+ tilo i mo
du
(2n + 1)b
22.
Ja + bu
Forms Involving a? ± u?, a > 0
inf
1
du =
arctan
a
1
u
+ C
23.
a2 + u?
a
u -
1
du = -
+ C
24.
du =
u? – a²
a?
u +
1
1
1
25.
(a?
2a (n - 1)(a² + u?)"-1
+ (2n - 3)
(a? + u?)n-1
du
n + 1
Forms Involving Ju? + a', a > 0
a² In\u + Ju* ± a*) + c
26.
u Ju? ± a² du =
u(2u? = a*) /u? ± a² – a* In|u + Ju ± a*]] + c
27.
(ad
/u² + a²
du 3D
Ju + a²
Ja + Ju? + a?
+ C
28.
- a In
Ju|
+ C
29.
du = Ju? - a? - a arcsec
а
grieleval zuo
u² ± a²
u? ± a?
u?
Inļu
du =
+ C
30.
1
du = Inu + /
+ Ju? ± a + C
31.
%3D
Ju? + a²
a +
2 + at
1
arcsec
a
Jul
+ C
32.
du =
+ C
33.
du =
a
Jut ± a') + C
u?
34.
+t
Ju² ± a²
u² ± a²
+ C
a?u
1
1
36.
(u² ± a²)³/2
du = T-
35.
u? Ju? + a²
du =
a2.
+ C
Forms Involving Ja? – u?, a > 0
37. a- du = (-7+d soia) + c
- u? + a? arcsin
u? Ja? – u² du =
a?) Ja? - u? + at arcsin
+ C
38.
A5
Appendix B
Integration Tables
la + Ja? - u?
Va? - u?
du =
39.
du = Ja? - u? - al
+ C 40.
arcsin
a
+ C
u2
1
42. S =+
41.
du = arcsin
+ C
1
+ C
Ja? - u?
du =
uJa?
u?
a²-u?
a?u
1
du =
Va? – u?
43.
-u/a? - u? + a? arcsin
+ C
44.
du =
+ C
u2.
1
du =
a? Ja? - u
45.
(a? - u²)3/2
+ C
Forms Involving sin u or cos u
46.
sin u du = - cos u + C
47.
cos u du = sin u + C
48.
sin? u du =
- sin u cos u) + C
49.
cos? u du =
+ sin u cos u) + C
sin"-1 u cos u
cos" -1 u sin u
n -
50.
sin" u du =
sin"-2 u du
51.
cos" u du =
cos"-2 u du
52.
u sin u du == sin u - u cos u + C
53.
u cos u du = cos u + u sin u + C
54.
sin u du = - u" cos u + nu"-1 cos u du
55.
u" cos u du = u" sin u -
un-1 sin u du
56.
du = tan u sec u + C
57.
du = - cot u + csc + C
1 + sin u
1+ cos u
58.
du =
In tan u| + C
sin u cos u
Forms Involving tan u, cot u, sec u, or csc u
59.
tan u du = - In]cos u| + C
60.
cot u du = In sin u + C
itoH nt
61.
sec u du =
In/sec u + tan u + C
62.
csc u du = In|csc u – cot u +C or
csc u du =
- In|csc u + cot u + C
63.
tan? u du = -u + tan u + C
64.
cot? u du = -u - cot u + C
65.
sec2 u du = tan u + C
66.
csc? u du = - cot u + C
tan"-1
68.
cot"-1u
67.
tan"-2 u du, n # 1
cot" u du =
cot"-2 u du, n # 1
tan" u du =
n - 1
n - 1
secn-2
1
n -
+
n -
69.
u tan u
sec"-2 u du, n + 1
sec" u du =
csch-2
u cot u
csc"-2 u du, n# 1
70.
csc" u du =
A6
Appendix B Integration Tables
+ In/cos u ± sin u|) + C
7 In|sin u ± cos ul) +
72.
du =
1+ tan u
du =
1+ cot u
71.
1
du = u + cot u + csc u + C
74.
du = u - tan u + sec u + C
73.
1+ sec u
1+ csc u
Forms Involving Inverse Trigonometric Functions
Vī - u² + C
75.
arcsin u du = u arcsin u + /1 - u? + C
76.
arccos u du = u arccos u -
arctan u du = u arctan u - In/1 + u? + C
arccot u du = u arccot u + In/1 + u2 + C
77.
78.
In|u +
+ Ju? – 1| + C
Inu + Ju? – 1| + c
79.
arcsec u du = u arcsec u -
80.
arccsc u du = u arccsc u +
Forms Involving e"
e" du = e" + C
82.
ue" du = (u - 1)e" + C
du = u - In(1 + e") + C
1 + elu
83.
u"e" du = u"e" - n
u" - 'e" du
84.
85.
eau sin bu du =
(a sin bu - b cos bu) + C
86.
ea" cos bu du =
(a cos bu + b sin bu) + C
a? + b?
a2 + b2
Forms Involving In u
In u du = u(-1 + In u) + C
u In u du =
u?
-1+2 In u) + C
87.
88.
89.
u" In u du =
nt uzl-1+ (n + 1)In u] + C, n+ -1
So
Sa
90.
(In u)? du = u[2 - 2 In u + (In u)²] + C
91.
(In u)" du = u(In u)" – n
(In u)"- du
Forms Involving Hyperbolic Functions
92.
cosh u du = sinh u + C
93.
sinh u du = cosh u + C
94.
sech? u du = tanh u + C
95.
csch? u du = - coth u + C
sech u tanh u du = - sech u + C
csch u coth u du = - csch u + C
96.
97.
Forms Involving Inverse Hyperbolic Functions (in logarithmic form)
du
du
In(u + Ju? ± a) + C
99.
a? - u?
la +
In
2a
%3D
98.
Ju ± a²
+ C
la -
a + Ja? ± u²
+ C
du
100.
lul
a
UJa² ±
CamScanner
Transcribed Image Text:3sec? x
dx
tan x(2+3 tan x)
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 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning