Use a change of variables or the table to evaluate the following definite integral. -2 √ x² ex³ +2 -3 +27 dx Click to view the table of general integration formulas. -2 S² ex³ +27 +27 dx= (Type an exact answer.) General Integration Formulas S 1 a 1 cos ax + C cos ax dx= - sin ax + C S sin ax dx = -- a S csc 2 ax dx = 1 cot ax + C a 1 2 ax dx=tan ax + C Ssec 2 ax a 1 sec ax tan ax dx = sec ax + C seca Seax dx = 1 eax + C dx a a Stan-1+C S dx = -a 1 2 a = sec а -1 + C, a > 0 a csct -- csc ax cot ax dx = 1 1 -- a csc ax + C -bx+C, b>0, b 1 Sbx dx = Inbb S. dx = sin -1+C, a>0 a

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...
Question
Use a change of variables or the table to evaluate the following definite integral.
-2
√ x² ex³ +2
-3
+27 dx
Click to view the table of general integration formulas.
-2
S² ex³ +27
+27 dx=
(Type an exact answer.)
Transcribed Image Text:Use a change of variables or the table to evaluate the following definite integral. -2 √ x² ex³ +2 -3 +27 dx Click to view the table of general integration formulas. -2 S² ex³ +27 +27 dx= (Type an exact answer.)
General Integration Formulas
S
1
a
1
cos ax + C
cos ax dx=
- sin ax + C
S
sin ax dx =
--
a
S
csc 2 ax dx =
1
cot ax + C
a
1
2 ax dx=tan ax + C
Ssec 2 ax
a
1
sec ax tan ax dx = sec ax + C
seca
Seax dx = 1 eax + C
dx
a
a
Stan-1+C
S
dx
=
-a
1
2 a
= sec
а
-1
+ C, a > 0
a
csct
--
csc ax cot ax dx =
1
1
--
a
csc ax + C
-bx+C, b>0, b 1
Sbx dx = Inbb
S.
dx
= sin -1+C, a>0
a
Transcribed Image Text:General Integration Formulas S 1 a 1 cos ax + C cos ax dx= - sin ax + C S sin ax dx = -- a S csc 2 ax dx = 1 cot ax + C a 1 2 ax dx=tan ax + C Ssec 2 ax a 1 sec ax tan ax dx = sec ax + C seca Seax dx = 1 eax + C dx a a Stan-1+C S dx = -a 1 2 a = sec а -1 + C, a > 0 a csct -- csc ax cot ax dx = 1 1 -- a csc ax + C -bx+C, b>0, b 1 Sbx dx = Inbb S. dx = sin -1+C, a>0 a
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