General Integration Formulas cos a cos ax dx = Ssec²ax 1 sin ax + C a 1 sec ax dx = - tan ax + C a Ssec axtan ax dx sec ax tan ax dx = Sex dx = S S a² dx +x² dx 1 a eax 1 == a x + C = 1 - a sec ax + C tan-1+C 1 - a sec a 1 a + C, a > 0 Jsina sin ax dx = csc 2 ax csc ax dx: csca 1 -- = - a 1 - cos ax + C a csc ax cot ax dx: Sbx dx = 1 In b S- dx 2 √a²-x² 2 cot ax + C - 1 a csc ax+C -bx+C, b>0, b#1 -1 x - = sin¯ ½ ½-½ + C, a + C, a > 0 - Use a change of variables or the table to evaluate the following definite integral. -2 +27 dx -3 Click to view the table of general integration formulas. -2 √ x² ex³ +27 dx = | (Type an exact answer.) -3
General Integration Formulas cos a cos ax dx = Ssec²ax 1 sin ax + C a 1 sec ax dx = - tan ax + C a Ssec axtan ax dx sec ax tan ax dx = Sex dx = S S a² dx +x² dx 1 a eax 1 == a x + C = 1 - a sec ax + C tan-1+C 1 - a sec a 1 a + C, a > 0 Jsina sin ax dx = csc 2 ax csc ax dx: csca 1 -- = - a 1 - cos ax + C a csc ax cot ax dx: Sbx dx = 1 In b S- dx 2 √a²-x² 2 cot ax + C - 1 a csc ax+C -bx+C, b>0, b#1 -1 x - = sin¯ ½ ½-½ + C, a + C, a > 0 - Use a change of variables or the table to evaluate the following definite integral. -2 +27 dx -3 Click to view the table of general integration formulas. -2 √ x² ex³ +27 dx = | (Type an exact answer.) -3
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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Transcribed Image Text:General Integration Formulas
cos a
cos ax dx =
Ssec²ax
1
sin ax + C
a
1
sec ax dx = - tan ax + C
a
Ssec axtan ax dx
sec ax tan ax dx =
Sex dx =
S
S
a²
dx
+x²
dx
1
a
eax
1
==
a
x + C
=
1
-
a
sec ax + C
tan-1+C
1
-
a
sec
a
1
a
+ C, a > 0
Jsina
sin ax dx =
csc 2 ax
csc ax dx:
csca
1
--
= -
a
1
-
cos ax + C
a
csc ax cot ax dx:
Sbx dx =
1
In b
S-
dx
2
√a²-x²
2
cot ax + C
-
1
a
csc ax+C
-bx+C, b>0, b#1
-1 x
- = sin¯ ½ ½-½ + C,
a
+ C, a > 0
-
Transcribed Image Text:Use a change of variables or the table to evaluate the following definite integral.
-2
+27 dx
-3
Click to view the table of general integration formulas.
-2
√ x² ex³ +27 dx = |
(Type an exact answer.)
-3
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