(Rev. C4) (6 points) Complete the perfect square and use the tables of integration to integrate. one \\ fin enidaffi maffe momurgizes aid timdue vox will bebrommood and xvx2+ 6x+ 3 dx Indicate the number of the integral you are applying from Appendix C of your textbook. Give your final answer in terms of x.Appendix C Integration Formulas Table 1 Integration Formulas Integrals Involving u" 1. of du = 1 * - 1 2 u' du = - dau = Injul Integrals Involving a + bu, a * 0 and b # 0 du = 1 Inla + bul * to du = * - loja + bul at boy du = (a + bu)? _2a(a + bu) Ina + bul 6. ) (a + but ) = du = = (Inla + bul + a a + bu or du = 7 . Ta + bu ) ? ( a + bu) b'(a + bu) - Inja + bul 8. "( a + bu )" du = - (a + bu)"+2 a(a + bu) #+1 ( " + 2)b (n + 1)b2 . " # -1, -2 " ( a + bu) du = - In " 10 . 7 ( a + bu ) 1 b a+ bu au " ( a + bu) = du = = a(a + bu) la+ bu 12 3 or ( a + bu) ; du = - a + 2bu 2b a + bu aw( a + bu ) u Integrals Involving a' - w', a > 0 13. du = 1In 4 -d lu+ al 14.du = L Inu + a Integrals Involving (a + bu) and (c + du), b # 0,d + 0, and ad - bc + 0 15. (a + bu) (e + )(et du ) dur = ad - be a + bul 16. / (a + bu ) (c + du ) du = ad - be ({ In a + bul - Inle + duel ) 17. J (a + bu ) (c + du ) du = ba " - ad - be (" lola + bul - Inle + duel) [Note: The constant of integration is omitted for each integral, but must be included in any particular application of a formula. The variable u is the variable of integration; all other symbols represent constants.] 547548 APPENDIX C Integration Formulas Table 1 Integration Formulas Continued 18. (at bu) ? (c + du) C + du du = ad - be a + bu ( ad - be)? a + bu 19 . (a + bu) (c + dur ) c + du b(ad - be) a + bu (ad - bc)? a + bu 20. a + but du - bu - ad - be Inlc + duel Integrals Involving Va + bu, a # 0 and b # 0 21. Vat budu - 2V (a + bu) 3b 22. "Va + bu du = 2(3bu - 2a) 156 - V(a + bu) 23. w Va + budu - 2(15bur - 12abu + 807) V(a + bu) 10563 24. - du - 2Va + bu Vat bu b 25. 2(bu - 2a) Vat bu "Va + bu 362 26. -du = 2(3bur - 4abu + 80 ) + bu Vat bu 1563 27. In Vat bu - Val Vat bu = du Va Va+ bu + Val' 28. Vat bu b Va + bu - Val w/ Va + bu 20 Va Va+ bu + Val' Integrals Involving Va - w,a > 0 29. du = 1Inat Va - 30. du = Va - w 31. Va - "d = Va - i - alot a- Integrals Involving Va' + a',a> 0 32. Vir ta du = ; ( uVir + a + a Inju + Vital) 33. (w Vir + a du = y [u( 207 + a ) Vir + a - a" lalu + Vir + all 34. Vir to dis = Vita - amat Vita 35. Virtad - - Vir to + Inju+ Vital 36. Vita du = Inju + Vir + al 37. Vita du = - In- la + Vita 38. -du = = (" Vi + a - a Inju + Vir + al) 39. [Note: The constant of integration is omitted for each integral, but must be included in any particular application of a formula. The variable u is the variable of integration; all other symbols represent constants.]APPENDIX C Integration Formulas 549 Table 1 Integration Formulas Continued Integrals Involving Vir' - a,a> 0 40. Vir - a du = ; ( wVi - a - olaju+ Viz-al) 41. ( 17 Vir - a du = = [u(207 - 07 ) V/i - a - a Inlu + Vir - all 43. V - a du = Inju + Vi - al 45. du= a u Integrals Involving ", a * 0 46. " du = = 48. + du = " - Linkc+ del. c # 0 Integrals Involving In a 49. Inudu = ulnu - u so. flu du = ; (In u)? 51. of In udu = uft ( n + 1)? " * -1 52. (Inu)" du = "(Inu)" - n / (lau)"du Integrals Involving Trigonometric Functions of au, a # 0 53. sin au du = -- cos au 54. cos au du = - sin au 55. tan au du = -- In|cos cut 56. cox au du = = In| sin cul 57. sec au du = - In/sec au + tan au) 58. csc au du = = Injess au - cot aul = 4 - 1 sin 2qu 59. (sin an) ? du = " - 60. (cos an)? du = " + - sin 2au 61. (sin au)" du = (sinau)" 'cos an + "-(sinau)" ? du, n * 0 62. (cos am)" du = sin an(cos au)"-1 + "-1 (cos au)" 2 du, n *0 Note: The constant of integration is omitted for each integral, but must be included in any particular application of a formula. The variable a is the variable of integration; all other symbols represent constants.]