Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
a) state the number of the
Transcribed Image Text:1.
118
Basic Integration Formulas
Substitution Formulas
1.
x+1+C
1.
5.
= np un
n+ 1
+ C
%3D
n + 1
1.
xp uX
xp
In |x| + C
6.
u-1 du =
%3D
%3D
2.
xp
%3D
%3D
np
1.
= xp xpa
a.
3.
ex dx = ex + C
4.
7.
e" du = e" + C
%3D
Integration by Parts Formula
8.
ap n
np a
an =
A Short Table of Integrals
Forms Involving ax + b:
9.
xp.
a.
In Jax + b| + C
%3D
10.
1.
+ C
%3D
xp
1.
bc
In |cx + d| – ° n|ax + b1) + c
11.
%3D
(ax + b)(cx + d)
-
= xp
12.
1.
xp
xv)x
+ C
In
2ax - 4b
Forms Involving vax + b:
13.
%3D
= xp
3a?
9 + xxx
q^ – 9 + xvX
q +9 + xxx
14.
1.
= xp
(0 < 4)
이 -
Vr? ± a² ± In |x + Vx? ± a² | + C
Forms Involving x- a?
and a?
1.
xp
1.
a²
15.
+ C
16.
In
+ C
%3D
%3D
-
a.
Forms Involving yx + a²:
17.
%3D
1.
dx = In |x + Vx² ± a² | + C
18.
%3D
+ a?
Forms Involving Va² ± x²:
dx = Va? ± x² – a ln
a + Va? ± x?
+ C
19.
|
%3D
U-- = Xp:
a.
a + ya² ± x²
+ C
20.
1.
%3D
xva? ± x?
Forms Involving e ax
and In r:
1.
= xp mduX
| (In x)" dx = x(ln x)" – n | (In x)"-1 dx
21.
x"-leax dx
%3D
1.
x"+1 ln x
1.
+1+C
(n + -1)
23.
x" ln x dx =
%3D
+ u) _
See also page 604.
(n + 1)²
Trigonometric Formulas
sin x dx = -cos x + C
sec? x dx
= tan x + C
sec x tan x dx sec x + C
cos x dx =
= sin x + C
csc? x dx = - cot x + C
Csc x cot x dx = - csc x + C
Transcribed Image Text:-dp-
(2x+3)(1-x)
1.
a) Integral Number in the attached Table:
b) Values of the constants: a =
b =
;%3D
c) Plug in the constants to find the integral (show how you plugged in!):
d) Simplify your answer in part c):
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Similar questions
- 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.arrow_forwardSolve the integral by parts problemarrow_forwardFor each problem, a) state the number of the integral in the attached Table; b) state the values of the constant(s); C) plug in the values of the constants to find the integral; d) simplify.arrow_forward
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