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:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
Expert Solution

Step 1
As per guidelines we will solve first question only,
1.
Step by step
Solved in 2 steps

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