MATH 225 Calculus III
Exam : Integration Gateway
January 11, 2016
Name:
Section or time:
Do your work on separate paper. Points will be deducted for work done on this sheet. You do
not need to report your answers on this sheet. You are not allowed a calculator or notes. Answers
without work will not be graded. At least five problems must be completely correct for a pass.
1.
Z
2.
x5 − 5
2
dx
Z
6 cos (2x) sin (2x) dx
3.
Z
4.
√
Z
5.
5
dx
1 − 16x2
9 · 21−3x dx
Z
6 tan (9x) dx
6.
Z
cot (7x) csc (csc (7x)) cot (csc (7x)) dx
7.
Z
2x · 12x dx
1
MATH 225 Calculus III
Exam : Integration Gateway
January 11, 2016
Name:
Section or time:
Do your work on separate paper. Points will be deducted for work done on this sheet. You do
not need to report your answers on this sheet. You are not allowed a calculator or notes. Answers
without work will not be graded. At least five problems must be completely correct for a pass.
1.
Z
6 csc (x) cot (x) dx
2.
Z
2 cot (7x) dx
3.
4.
Z
Z
x−33 log13 x dx
7x7 x5 − 2x + 2 dx
5.
Z
6.
Z
7.
Z
4 · 226x dx
√
3
dx
49 − x2
sec2 (25x)
p
dx
1 − tan2 (25x)
2
MATH 225 Calculus III
Exam : Integration Gateway
January 11, 2016
Name:
Section or time:
Do your work on separate paper. Points will be deducted for work done on this sheet. You do
not need to report your answers on this sheet. You are not allowed a calculator or notes. Answers
without work will not be graded. At least five problems must be completely correct for a pass.
1.
Z
2.
√
3
dx
49 − x2
Z
5 cot (5x) dx
3.
Z
4.
x−25 log14 x dx
Z
3 sin (7x) cos (7x) dx
5.
6.
Z
6
dx
e2x
Z
csc (6x) csc (cot (6x)) cot (cot (6x)) dx
7.
Z
x6 − 8
3
2
dx
MATH 225 Calculus III
Exam : Integration Gateway
January 11, 2016
Name:
Section or time:
Do your work on separate paper. Points will be deducted for work done on this sheet. You do
not need to report your answers on this sheet. You are not allowed a calculator or notes. Answers
without work will not be graded. At least five problems must be completely correct for a pass.
1.
Z
2.
Z
3.
Z
4.
5.
6.
7.
Z
8 · e−2x dx
x40 log19 x dx
6 sec2 (5x)
dx
tan (5x) + 16
csc (81x) cot (81x)
p
dx
1 − csc2 (81x)
Z 14x1/5 + 9x7 dx
Z
Z
3 cos2 (2x) dx
√
7
dx
1 − 4x2
4
MATH 225 Calculus III
Exam : Integration Gateway
January 11, 2016
Name:
Section or time:
Do your work on separate paper. Points will be deducted for work done on this sheet. You do
not need to report your answers on this sheet. You are not allowed a calculator or notes. Answers
without work will not be graded. At least five problems must be completely correct for a pass.
1.
Z
2.
2 csc2 (3x)
dx
cot (3x) + 14
Z
5 cos (x) dx
3.
4.
Z
Z
24x7 + 35x6 csc2 3x8 + 5x7 + 17 dx
5.
6.
9x−4 3 + 8x + x3 dx
Z
5
dx
25 + x2
Z
(5x + 14) sin (3x) dx
7.
Z
7 · 12−4x dx
5
MATH 225 Calculus III
Exam : Integration Gateway
January 11, 2016
Name:
Section or time:
Do your work on separate paper. Points will be deducted for work done on this sheet. You do
not need to report your answers on this sheet. You are not allowed a calculator or notes. Answers
without work will not be graded. At least five problems must be completely correct for a pass.
1.
Z
2.
3
dx
e8x (2 + 3e−8x )
Z
3.
4.
5.
3
dx
1 + 25x2
Z
Z 3
dx
e3x
8x1/6 + 23x9 dx
Z
(2x + 19) cos (3x) dx
6.
Z
9 tan (2x) dx
7.
Z
7 sin (5x) cos (5x) dx
6
MATH 225 Calculus III
Exam : Integration Gateway
January 11, 2016
Name:
Section or time:
Do your work on separate paper. Points will be deducted for work done on this sheet. You do
not need to report your answers on this sheet. You are not allowed a calculator or notes. Answers
without work will not be graded. At least five problems must be completely correct for a pass.
1.
Z
(8x + 4) cos (2x) dx
2.
3.
Z
Z
4 cos6 (4x) sin (4x) dx
2 42x5 − 57x−4
4.
Z
5.
√
Z
6.
Z
7.
Z
7x6 + 19x−3 + 8
8
dx
81 − x2
3 · 405x dx
x4 − 7
2
dx
8 sec2 (7x)
dx
tan (7x) + 17
7
1/6
dx
MATH 225 Calculus III
Exam : Integration Gateway
January 11, 2016
Name:
Section or time:
Do your work on separate paper. Points will be deducted for work done on this sheet. You do
not need to report your answers on this sheet. You are not allowed a calculator or notes. Answers
without work will not be graded. At least five problems must be completely correct for a pass.
1.
Z
5
dx
e9x (8 + 4e−9x )
2.
Z
3.
7
dx
143x
Z
6 cos (x) dx
4.
Z
5.
x29 log13 x dx
Z
6 cot (5x) dx
6.
7.
Z
Z √
4
dx
36 − x2
14x1/4 + 28x−18 dx
8
MATH 225 Calculus III
Exam : Integration Gateway
January 11, 2016
Name:
Section or time:
Do your work on separate paper. Points will be deducted for work done on this sheet. You do
not need to report your answers on this sheet. You are not allowed a calculator or notes. Answers
without work will not be graded. At least five problems must be completely correct for a pass.
1.
Z
2.
54x5 + 27x2
dx
9x6 + 9x3 + 9
Z
8 sec (x) tan (x) dx
3.
Z
x7 sin 4x9 + 15 dx
4.
Z
5
dx
16 + x2
5.
Z
6 · 172x dx
6.
7.
Z
x9 − 7
2
dx
Z
(8x + 9) sin (8x) dx
9
MATH 225 Calculus III
Exam : Integration Gateway
January 11, 2016
Name:
Section or time:
Do your work on separate paper. Points will be deducted for work done on this sheet. You do
not need to report your answers on this sheet. You are not allowed a calculator or notes. Answers
without work will not be graded. At least five problems must be completely correct for a pass.
1.
2.
Z
Z
x18 log8 x dx
4 csc (6x) cot (6x) (9 + 17 csc (6x))1/8 dx
3.
Z
2 tan (6x) dx
4.
Z
5.
Z
6.
7.
sec2 (49x)
dx
1 + tan2 (49x)
Z
Z
5
dx
414x
6 sec2 (8x) dx
3x−2 x7 − 6x + 8 dx
10