1. 2x +3 a) Integral Number in the Table: b) Values of the constants: c) Plug in the constants to find the inte d) Simplified Answer:
1. 2x +3 a) Integral Number in the Table: b) Values of the constants: c) Plug in the constants to find the inte d) Simplified Answer:
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 77E
Related questions
Question
Use the attached table of integrals to find the following integrals. For each problem, a) state the number of the integral in the table l; b) state the values of the constant(s); c) plug in the values of the constants to fine the integral; d) simplify.
Transcribed Image Text:dx
1.
2x +3
a) Integral Number in the Table:
b) Values of the constants:
c) Plug in the constants to find the integral (show how you plugged in!):
d) Simplified Answer:
2.
a) Integral Number in the Table:
b) Values of the constants:
c) Plug in the constants to find the integral (show how you plugged in!):
d) Simplified Answer:
Transcribed Image Text:Substitution Formulas
Basic Integration Formulas
1. frd- c
1
u*+1 + C
(n -1)
5.
u" du =
(n -1)
n+1
= In |x| + C
du
duD
"- In ju| + C
2.
x'dx
dx =
6.
u- du =
7. fra-rsc
3.
dx
4.
Integration by Parts Formula
8.
dv uv-
o du
A Short Table of Integrals
Forms Involving ax + b:
dx
ax + b
In lax + b| + C
9.
1
In
bc
1
ax +
10.
dx =
+ C
(ax + b)(cx + d)
ad
cx + d
1
dx =
(ax + b)(cx + d)
In Jex + d - 2inlax + b1) + c
11.
ad - bc \c
1
12.
dx =
In
+ C
x(ax + b)
2ax - 4b
Forms Involving vax + b:
dx 3D
Vax + b
Vax + b + C
3a?
13.
Vax +b-Vb
1
dx%3D
xVax + b
1
14.
In
+ C
(b> 0)
Vax + b+ Vb|
Forms Involving x - a²
and a? - x:
15.
dx =
+ C
16.
2
Forms Involving vr² ± a²:
Va? t af dx =Vx² =
17.
1
18.
dx = In x+ Vx? # a² + C
Va“ ± x* dx = Va? ± x- a ln
a+ Va? + x²
+ C
Forms Involving va² ± x²:
19.
a + Va? + x2
+ C
20.
= xp
Forms Involving er
and In x:
(In x)" dx x(ln x)" – n (In x)n-1 dx
21.
x"e
x-leax dx
22.
Srinsd
1
x+1 + C
g+1 In x -
(n -1)
23.
(n + 1)2
Trigonometric Formulas
See also page 604.
sec? x dx = tan x + C
sec x tan x dx = sec x + C
sin x dx = - cos x + C
cos x dx = sin x + C
csc x dx = -cot x + C
cSc x cot x dx = - csc x + C
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