Odd Ch 7 Review Problem methods
21. Parts done two times. First time u=x2, and second time u=x.
23. Parts with u=ln x.
25. Parts done two times. First time u=(ln x)2, and second time u=ln x.
27.Elementary function. e.5-.3t=e.5/e.3t=e.5*e-.3t. Since e.5 is a constant, pull it out of the integral and just
deal with e-.3t.
29.Substitution with u=4-x2
31. Substitution with u= sqrt(y)
33.Tricky parts. Parts with u=cos x, and then use the trig substitution sin2x=1-cos2x in the resulting
integral. You then bring the integral of cos2x to the left side of the equation since it can be combined
with the original problem. Simplify by dividing by 2.
35.Substitution with u=2x-6.
37. Elementary function. Foil, divide, and then integrate.
39. Elementary function. Divide and then integrate.
41. Use the trig identity then Substitution with u=cos x.
43. Substitution with u=x2+1.
45. Substitution with u=2x.
47. Substitution with u=cos 5x.
49. Substitution with u= t - 10 and also rewrite that as t= u + 10.
51. Parts with u= x.
53. Substitution with u=x2.
55. Rewrite 9 + u2 as 9[ 1 + (u/3)2]. Substitution with u=u/3.
57. Substitution with u=ln x.
59. Substitution with u=2x.
61. Elementary function. Divide into two fractions, simplify, and then integrate.
63. Substitution with u=ln x.
65. Substitution with u=sqrt( x2+1)
67. Parts with u=r.
69. Substitution with u=sqrt(2x) + 3.
71. Foil and separate the trinomial into three separate integrals. The first and last are elementary
functions. The middle one uses Parts with u=x.
73. Don’t do. Uses Integral Table in back of book.
75. Partial fractions.
77. Parts done twice with u= e-ct first time and second time. You have an integral the same as the original
problem so combine these terms on the left side and divide the whole equation by 2.
79. Don’t do. Uses Integral Table in back of book.
81. Don’t do. Uses Integral Table in back of book.
83. Don’t do. Uses the kind of Partial Fractions we didn’t do yet.
85. Substitution with u=ax2+2bx+c.
87. Substitution with u=22+1.
89. Elementary function. Multiply and then integrate.