dx (2x + 3)(1–x) 1. a) Integral Number in the attached Table: b) Values of the constants: a = b = c) Plug in the constants to find the integral (show how you plugged in!): d) Simplify your answer in part c):
dx (2x + 3)(1–x) 1. a) Integral Number in the attached Table: b) Values of the constants: a = b = c) Plug in the constants to find the integral (show how you plugged in!): d) Simplify your answer in part c):
dx (2x + 3)(1–x) 1. a) Integral Number in the attached Table: b) Values of the constants: a = b = c) Plug in the constants to find the integral (show how you plugged in!): d) Simplify your answer in part c):
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.
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):
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
