← E a L 1. Find the indefinite integral of each of the following: a. fx sin2x dx b. [x² sin 2xdx d. S XCOS Xdx e. fx lnx dx g. ²2te-²t dt Find the indefinito integral of onch of the following S | xe Xdx f. ¹₂te²t dt C. хр,

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Find the indefinite integral of each of the following:
a. fx sin2x dx
x² sin 2xdx
d. [xc
g. ²2te-2tdt
a.
j.
g. S
2. Find the indefinite integral of each of the following:
Se5x dx
b. [ sin4xdx
3x²
d. ſ. dx
x³
X +5
XCOS xdx
e√x
dx
√x
(e*+1)7e* dx
a.
d. S
a.
b.
m. By using the substitution t= x−1, find
n. By using the substitution x= 3sint, find
X+3
(x+1)(x+2)
x³
x+3x+2
3. Find the integral of each of the following:
X-9
2x²-3x+1
dx
dt
ICON 2202
b.
= kx
=
e. fx lnx dx
6xt²
C
e.
dx
|||
h. [x²√x³ +2dx
k. [xcos(x² + 1) dx
COS X
dx
1+ sin x
dx b. S
e.
2x² +7x+7
X+2
a
O
X-2
(x-1)²
1
9-²
dx
dx
c. S
f. ²te²t dt
C.
[3cos 3xdx
1
f. S dx
xln x
dx
%
3x²
(x³
3
+10) ³
I. [ e3cos2x sin 2xdx
.dx.
C.
4. Find the general solution of the following differential equation:
dx
dt
f.
xe Xdx
S
x² +3
x² + 3x
2
X
X-1
2
4x².
<
+ X
dx
-dx
dx
Page 1
Transcribed Image Text:← 1. Find the indefinite integral of each of the following: a. fx sin2x dx x² sin 2xdx d. [xc g. ²2te-2tdt a. j. g. S 2. Find the indefinite integral of each of the following: Se5x dx b. [ sin4xdx 3x² d. ſ. dx x³ X +5 XCOS xdx e√x dx √x (e*+1)7e* dx a. d. S a. b. m. By using the substitution t= x−1, find n. By using the substitution x= 3sint, find X+3 (x+1)(x+2) x³ x+3x+2 3. Find the integral of each of the following: X-9 2x²-3x+1 dx dt ICON 2202 b. = kx = e. fx lnx dx 6xt² C e. dx ||| h. [x²√x³ +2dx k. [xcos(x² + 1) dx COS X dx 1+ sin x dx b. S e. 2x² +7x+7 X+2 a O X-2 (x-1)² 1 9-² dx dx c. S f. ²te²t dt C. [3cos 3xdx 1 f. S dx xln x dx % 3x² (x³ 3 +10) ³ I. [ e3cos2x sin 2xdx .dx. C. 4. Find the general solution of the following differential equation: dx dt f. xe Xdx S x² +3 x² + 3x 2 X X-1 2 4x². < + X dx -dx dx Page 1
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