Basic Integration Formulas Substitution Formulas 1. - x+1 + C (n -1) 5. 4" du ** + C (n +-1) 2. In |지 + 0 6. %3D = np 3. + C 4. 7. du=e + C Integration by Parts Formula 8. du = uD - du A Short Table of Integrals Forms Involving ax + b: 9. ax + b %-in lax+ b| + c dx = 1 ax + b In |cx+d 10. dx%3D (ax + b)(cx + d) + C ad - be 1 dx = ad (inlex +d-injax + bi) + 11. (ax + b)(cx + d) 1 dx- Flax + b) 12. + In ax +b + C Forms Involving vax + b: 13. Vax + dx = 9. 2ax - 4b Vax + b+ C 3a2 yax + b- Vb In 1 14. - xp + C (b > 0) Vax + b + b Forms Involving x-a and a- + C * +a 15. dx = In 16. In 2a + C 2a Forms Involving Vr t a Vr dx =V a Inx +Vx? + + C 17. 18. dx= In x + x +C
Basic Integration Formulas Substitution Formulas 1. - x+1 + C (n -1) 5. 4" du ** + C (n +-1) 2. In |지 + 0 6. %3D = np 3. + C 4. 7. du=e + C Integration by Parts Formula 8. du = uD - du A Short Table of Integrals Forms Involving ax + b: 9. ax + b %-in lax+ b| + c dx = 1 ax + b In |cx+d 10. dx%3D (ax + b)(cx + d) + C ad - be 1 dx = ad (inlex +d-injax + bi) + 11. (ax + b)(cx + d) 1 dx- Flax + b) 12. + In ax +b + C Forms Involving vax + b: 13. Vax + dx = 9. 2ax - 4b Vax + b+ C 3a2 yax + b- Vb In 1 14. - xp + C (b > 0) Vax + b + b Forms Involving x-a and a- + C * +a 15. dx = In 16. In 2a + C 2a Forms Involving Vr t a Vr dx =V a Inx +Vx? + + C 17. 18. dx= In x + x +C
Basic Integration Formulas Substitution Formulas 1. - x+1 + C (n -1) 5. 4" du ** + C (n +-1) 2. In |지 + 0 6. %3D = np 3. + C 4. 7. du=e + C Integration by Parts Formula 8. du = uD - du A Short Table of Integrals Forms Involving ax + b: 9. ax + b %-in lax+ b| + c dx = 1 ax + b In |cx+d 10. dx%3D (ax + b)(cx + d) + C ad - be 1 dx = ad (inlex +d-injax + bi) + 11. (ax + b)(cx + d) 1 dx- Flax + b) 12. + In ax +b + C Forms Involving vax + b: 13. Vax + dx = 9. 2ax - 4b Vax + b+ C 3a2 yax + b- Vb In 1 14. - xp + C (b > 0) Vax + b + b Forms Involving x-a and a- + C * +a 15. dx = In 16. In 2a + C 2a Forms Involving Vr t a Vr dx =V a Inx +Vx? + + C 17. 18. dx= In x + x +C
Please answer it not graded asked to Use the attached Table of Integrals to find the following integrals. For 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. Thanks
Transcribed Image Text:Basic Integration Formulas
Substitution Formulas
* fra
1.
+ C
(n *-1)
5.
(1 + -1)
n+1
du
In u|+C
2.
6.
%3D
3.
4.
7.
Integration by Parts Formula
8.
i du = up -
v du
A Short Table of Integrals
Forms Involving ax + b:
9.
ax + b
dx =
In ax + b + C
10.
dx =
(ax + b)(cx + d)
In
+ C
ad - be
Cx + d
1
dx =
(ax + b)(cx + d)
in lex + d|-inlax + b) +
1.
ad-be \c
1
12.
In
ax + b
+C
x*(ax + b)
Forms Involving vax + b:
2ax - 4b
13.
dx 3D
VIEX +b+ C
Vax + b- VE
In
VIEX + b + yb
(b > 0)
14.
+ C
Forms Involving r-a
and a - r
15.
dx =
In
+C
16.
+ C
2a
Forms Involving va + a
17.
18.
dx = In x + Vx ± +C
Forms Involving Va
19.
dx = Va = -a In
20.
dx =- In
Forms Involving e
and In
21.
22.
(In x dx x(ln x-
(In x dx
23.
*in
In x
Irigonometric Tormulas
See also page fi
sin x da
s d= tan C
sec a tan x dx sec E
COS da= sin x +C
Transcribed Image Text:2.
*/4-x2
a) Integral Number in the attached Table:
b) Values of the constants: a =
d =
(Fill in the blanks. If there is no such
constant, leave the entry blank.)
CC =
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.
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