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1. 2x +3 a) Integral Number in the Table: b) Values of the constants: c) Plug in the constants to find the inte d) Simplified Answer:

1. 2x +3 a) Integral Number in the Table: b) Values of the constants: c) Plug in the constants to find the inte d) Simplified Answer:

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the attached table of integrals to find the following integrals. For each problem, a) state the number of the integral in the table l; b) state the values of the constant(s); c) plug in the values of the constants to fine the integral; d) simplify.
dx 1. 2x +3 a) Integral Number in the Table: b) Values of the constants: c) Plug in the constants to find the integral (show how you plugged in!): d) Simplified Answer: 2. a) Integral Number in the Table: b) Values of the constants: c) Plug in the constants to find the integral (show how you plugged in!): d) Simplified Answer:
Transcribed Image Text:dx 1. 2x +3 a) Integral Number in the Table: b) Values of the constants: c) Plug in the constants to find the integral (show how you plugged in!): d) Simplified Answer: 2. a) Integral Number in the Table: b) Values of the constants: c) Plug in the constants to find the integral (show how you plugged in!): d) Simplified Answer:
Substitution Formulas Basic Integration Formulas 1. frd- c 1 u*+1 + C (n -1) 5. u" du = (n -1) n+1 = In |x| + C du duD "- In ju| + C 2. x'dx dx = 6. u- du = 7. fra-rsc 3. dx 4. Integration by Parts Formula 8. dv uv- o du A Short Table of Integrals Forms Involving ax + b: dx ax + b In lax + b| + C 9. 1 In bc 1 ax + 10. dx = + C (ax + b)(cx + d) ad cx + d 1 dx = (ax + b)(cx + d) In Jex + d - 2inlax + b1) + c 11. ad - bc \c 1 12. dx = In + C x(ax + b) 2ax - 4b Forms Involving vax + b: dx 3D Vax + b Vax + b + C 3a? 13. Vax +b-Vb 1 dx%3D xVax + b 1 14. In + C (b> 0) Vax + b+ Vb| Forms Involving x - a² and a? - x: 15. dx = + C 16. 2 Forms Involving vr² ± a²: Va? t af dx =Vx² = 17. 1 18. dx = In x+ Vx? # a² + C Va“ ± x* dx = Va? ± x- a ln a+ Va? + x² + C Forms Involving va² ± x²: 19. a + Va? + x2 + C 20. = xp Forms Involving er and In x: (In x)" dx x(ln x)" – n (In x)n-1 dx 21. x"e x-leax dx 22. Srinsd 1 x+1 + C g+1 In x - (n -1) 23. (n + 1)2 Trigonometric Formulas See also page 604. sec? x dx = tan x + C sec x tan x dx = sec x + C sin x dx = - cos 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:Substitution Formulas Basic Integration Formulas 1. frd- c 1 u*+1 + C (n -1) 5. u" du = (n -1) n+1 = In |x| + C du duD "- In ju| + C 2. x'dx dx = 6. u- du = 7. fra-rsc 3. dx 4. Integration by Parts Formula 8. dv uv- o du A Short Table of Integrals Forms Involving ax + b: dx ax + b In lax + b| + C 9. 1 In bc 1 ax + 10. dx = + C (ax + b)(cx + d) ad cx + d 1 dx = (ax + b)(cx + d) In Jex + d - 2inlax + b1) + c 11. ad - bc \c 1 12. dx = In + C x(ax + b) 2ax - 4b Forms Involving vax + b: dx 3D Vax + b Vax + b + C 3a? 13. Vax +b-Vb 1 dx%3D xVax + b 1 14. In + C (b> 0) Vax + b+ Vb| Forms Involving x - a² and a? - x: 15. dx = + C 16. 2 Forms Involving vr² ± a²: Va? t af dx =Vx² = 17. 1 18. dx = In x+ Vx? # a² + C Va“ ± x* dx = Va? ± x- a ln a+ Va? + x² + C Forms Involving va² ± x²: 19. a + Va? + x2 + C 20. = xp Forms Involving er and In x: (In x)" dx x(ln x)" – n (In x)n-1 dx 21. x"e x-leax dx 22. Srinsd 1 x+1 + C g+1 In x - (n -1) 23. (n + 1)2 Trigonometric Formulas See also page 604. sec? x dx = tan x + C sec x tan x dx = sec x + C sin x dx = - cos x + C cos x dx = sin x + C csc x dx = -cot x + C cSc x cot x dx = - csc x + C
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