Integration Problems to Work on in Preparation for the Technique

Integration Problems to Work on in Preparation for the Technique Test
UPDATED
October 10, 2002
1.
R
x sec2 x dx
27.
R
√ x
x2 +1
2.
R
4x+4
2x+1 dx
28.
R
ex
e2x −4
dx
3.
R
7xex dx
29.
R
e2x
e2x −4
dx
4.
R
dx
x2 +6x+9
30.
R ln 3
31.
R
x+5
x2 −2x−3
32.
R
x2 +3
x2 +1
33.
R
x2 ex dx
34.
R
3 tan(2x) dx
35.
R
etan x sec2 x dx
36.
R
cos x sin(2 sin x) dx
37.
R
− ln(1+x)
(1+x)2 dx
38.
R
2
x2 +2x+1 dx
39.
R
1
x(x+2) dx
40.
R
x2
(1−9x2 )(3/2)
41.
R
2
5.
R 10
6.
R9√
7.
R
8.
R
9.
R
10.
R
11.
R
12.
R
13.
R
14.
R
15.
R
cos(x2 ) dx
16.
R
cos2 x dx
0
dx
x
√ ex
e +4
dx
3
−10
sin(x ) dx
4 + 3x dx
√
ex 1 − e2x dx
1
ex sin x dx
x ln x dx
dx
dx
3
2
sin (7x) dx
4x3 +3x2 +2x+1
x4 +x3 +x2 +x+1 dx
6x+3
(x−1)(x−2)(x−3) dx
2
x cos(x ) dx
2
x cos x dx
(Use series.)
dx
3x cos x dx
√
√
(x x2 + 2x + x2 + 2x )dx
17.
R
x3 cos x2 dx
42.
R
18.
R
cos3 x dx
43.
Re
19.
Re
44.
R
sin(ln(x)) dx
45.
R
3
x2 (x2 +9) dx
46.
R
x3
x2 +1 dx
47.
R
dx
x3 +x
1
ln x dx
(ln x)2 dx
1
sin(ln(x))
dx
x
20.
R
21.
R
22.
R e3
23.
R
x ln(x2 + 1) dx
48.
R
sin(x)dx
cos2 (x)−5 cos(x)+4
24.
R
x2 −1
x2 +1
dx
49.
R
e√ x
dx
x
25.
R
x2 +1
x2 −1
dx
50.
R√
26.
R
x
x4 +1
dx
51.
R
(ln x)2
x
e
dx
1
x ln x
dx
√
1
9 − 4x2 dx
x+1
x2 +1 dx
2
2
52.
R
2xe(x+1) + 2e(x+1) dx
53.
R
cos2 (x) − sin2 (x) dx
54.
R
55.
R
x sin((x + 1)(x − 1)) dx
56.
R
57.
R
58.
R π/2
59.
Re
60.
R
sin x cos x dx
61.
R
dx
x ln x ln(ln x)
62.
R
dx
(1−x2 )3/2
√ x
dx
1−x2
R
84.
R1 √
R
x5 −1
x−1 dx
86.
R
2x((x2 + 1)2 + 1)2 dx
87.
1
88.
3
√x
dx
1−x2
89.
x2 ln x dx
90.
91.
sin3 (2x) dx
R √
64. ln x dx
R
65. xx+1
2 −4 dx
R
1
66. (x2 +1)
3/2 dx
63.
R
67.
R
ee
68.
R
cos(x)
1+sin(x)
69.
R
x3 +1
x2 −1
70.
R
1
x(x2 +a2 )
71.
R1
72.
R∞
73.
R
x
(x2 −a2 )3/2
74.
R
x(ln x)2 dx
75.
R1
76.
R
77.
R
78.
R1
0
√ 1
dx
1−x2
79.
R1
x5 ln x dx
80.
R2
81.
R
√ x
dx
x2 +3
82.
R
eln x dx
x
+x
1/2 x2
1
dx
dx
dx
dx
√1
1−x2
ln(x)
x2
1
0 1+x 13
dx
dx
dx
dx
tan2 x dx
1
2
ln 3
0
0
1
1
ex +e−x dx
1
e− x
x2
1 − x2 x2 dx
0
85.
−π/2
(x−1)dx
(x2 +1)(x+1)
83.
dx
2
cos(x) ln(sin(x)) dx
√
x dx
x+1
R √
( ln x/x) dx
R 2 x
x e dx
R
(sin x)3 dx
R
ln(x2 + 1) dx
R ln(ln x)
dx
x