19. c + du ( a + bu) ?( c + du) - du = - b(ad - bc) a + bu (ad - bc) ?" 2 In la+ bu 20. a + bu du = c+ du bu ad - be Inc + dul d d2 Integrals Involving Va + bu, a # 0 and b # 0 21. / Va + budu = 2V ( a + bu ) 3 3b 22. uva + budu = 2(3bu - 2a) 1562 - V ( a + bu ) 3 23. u Va + budu = 2(156217 - 12abu + 8a?) 10563 V(a + bu) 3 24. du = 2 Va + bu Va+ bu 25. du = 2(bu - 2a) Vatbu Va + bu 362 26. uz du = 2(3b u2 - 4abu + 8a2) Vat bu 1563 Va + bu 27. du = uva + bu = In 1 Va + bu - Val Va Va+ but Val a >o 28. = du = Va+ bu b u Va + bu = In |Va + bu - Val au 2aVa Va+ bu + Val' azo Integrals Involving Val - u2, a > 0 29. du = -1in a+ Va - u uVaz - up u 30. = du = Vaz - up au 31. Var - U du = Vaz - 12 - aln a + Vaz - 12 u Integrals Involving Vu2 + a2, a > 0 32 . Vu + a du = - ( uvu + a + a? Inlu + Vu + al) 33 . " Vu + a du = [u( 212 + a? ) Vu + a? - at Inlu + Vix + al] 34. [ Nuta du = Vita? - aIn a + Vu + a u u 35. "Vita= 12 Viita + Inlu + Vi+ all 36. du = Inlu + Vu + all 37. u u + a2 du = - In a la+ Vutar u 2 38. Vu+ a = du = = (uVuz + a2 - a Inju + Viz + all) 39. =du = Viita au [Note: The constant of integration is omitted for each integral, but must be included in any particular application of a formula. The varia the variable of integration; all other symbols represent constants.]A Table 1 Integration Formulas Continued Integrals Involving Vu2 - a, a > 40. ( Vit - a du = z (uVu - a - a Inlu + Vit- al) 4. ( Vu - a du = [u(21 - a?) Vu - a - a' Inju + Vit-all [ Nu - a = - Vu - a 42. u - + Inju + Vuz - a-] 1 43. du = Inju + Vu - a21 V1 - a2 44. du = = (uVu - a2 + a? Inju + Vu - a-]) Vuz - a2 45. du au Integrals Involving eau, a # 0 46. am du = 47 . weau du = Weau n / u- leal du a 48 . ac C+ doau du = " - - Inlc + deau, c # 0 Integrals Involving In u 50. In " du = = (In u) ? 19. In u du = ulnu - u 52. ( In u) " du = u(In u)" - n/ n # -1 51. u' In udu = int In u (n + 1 ) 2' Integrals Involving Trigonometric Functions of au, a # 0 54. cos au du = - sin au 53. sin au du = - - cos au 56. cot au du = = In(sin au) 55. tan au du - - In cos aul 58. / csc au du = - Injesc au - cotUse an integration table formula to nd I V m2 36633? . Clearly indicate the formula you used from the integration tables. MAKE SURE TO USE THE INTEGRATION TABLE in Appendix C