Question 1 1. Evaluate using integration by parts.   ln x -   + C x2 ln x -   + C x2 ln x -  x2 + C x ln x -  x + C 2 points Question 2 1. Evaluate using integration by parts.  x2e2x - xe2x +  e2x + C  x2e2x -  xe2x +  e2x + C x2e2x -  xe2x + C  x2e2x -  xe2x +  e2x + C  2 points Question 3 1. Evaluate. Assume u > 0 when ln u appears.      dy 2e4y + C  e4y + C 4e4y + C  e4y + C 2 points Question 4 1. Find the particular solution determined by the given condition.  fʹ(x) = 6x2 - 4x + 21; f(1) = 17 f(x) = 2x3 - 4x2 + 21x - 2 f(x) = 6x3 - 4x2 + 21x - 6 f(x) = 2x3 - 2x2 + 21x + 4 f(x) = 2x3 - 2x2 + 21x - 4    2 points Question 5 1. Find the particular solution determined by the given condition.  yʹ =   ; y = 21 when x = 1 y = 5 ln x + 21 y = ln x + 19 y = 5 ln x + 2.5 y = ln x + 21 2 points Question 6 1. Determine if the function is a solution to the given differential equation.  y = x ln x - 4x + 5; yʹʹ -   = 0. Yes No 2 points Question 7 1. Evaluate using integration by parts.  (x2 - x) ln (16x) -   + 2x + C (x2 - x) ln (16x) -   + x + C  ln (16x) -   + x + C (x2 - x) ln (16x) - x2 + x + C 2 points Question 8 1. Find the general solution for the differential equation.   = 4P P = 4eCt P = Ce4t P = Ce-4t P = Cet 2 points Question 9 1. Evaluate. Assume u > 0 when ln u appears.      dt  e-7t2 + C -   e-7t2 + C  e-7t2 + C -   e-7t2 + C 2 points Question 10 1. Find the general solution for the differential equation.  y ' = 72x2 - 20x 72x3 - 20x2 + C 24x3 - 20x2 + C 72x3 - 10x2 + C 24x3 - 10x2 + C 2 points Question 11 1. Find the general solution for the differential equation.  y ' = x - 16 2x2 - 16 + C  - 16x + C  - x + C x3 - 16x + C 2 points Question 12 1. Evaluate using integration by parts.  e4xdx (x - 8) e4x -   e4x + C (x - 8) e4x +   e4x + C 4(x - 8) e4x - 16 e4x + C (x - 8) e4x - e4x + C 2 points Question 13 1. Evaluate using integration by parts.  dx 5x(2x + 3)1/2 +  (2x + 3)3/2 + C 5x(2x + 3)1/2 -  (2x + 3)3/2 + C x(2x + 3)1/2 -  (2x + 3)3/2 + C 5x(2x + 3)1/2 - (2x + 3)3/2 + C 2 points Question 14 1. Write the first four elements of the sequence.    n 0, 2,  ,  2,  ,  ,  1,  ,  ,  0, 1,  ,  2 points Question 15 1. Evaluate. Assume u > 0 when ln u appears.      dx  + C  + C  + C (ln 6x)2 + C 2 points Question 16 1. Evaluate. Assume u > 0 when ln u appears.      dp  e5p2+ C -   e5p2 + C 7e5p2 + C -7e5p2 + C 2 points Question 17 1. Evaluate. Assume u > 0 when ln u appears.      dy  ln   + C 18 ln   + C 19 ln   + C   ln   + C 2 points Que ...

1. Question 1
1.
Evaluate using integration by parts.
ln x - + C
x2 ln x - + C
x2 ln x - x2 + C
x ln x - x + C
2 points
Question 2
1.
Evaluate using integration by parts.
x2e2x - xe2x + e2x + C

2. x2e2x - xe2x + e2x + C
x2e2x - xe2x + C
x2e2x - xe2x + e2x + C
2 points
Question 3
1.
Evaluate. Assume u > 0 when ln u appears.
dy
2e4y + C
e4y + C
4e4y + C
e4y + C
2 points

3. Question 4
1.
Find the particular solution determined by the given condition.
fʹ(x) = 6x2 - 4x + 21; f(1) = 17
f(x) = 2x3 - 4x2 + 21x - 2
f(x) = 6x3 - 4x2 + 21x - 6
f(x) = 2x3 - 2x2 + 21x + 4
f(x) = 2x3 - 2x2 + 21x - 4
2 points
Question 5
1.
Find the particular solution determined by the given condition.
yʹ = ; y = 21 when x = 1

4. y = 5 ln x + 21
y = ln x + 19
y = 5 ln x + 2.5
y = ln x + 21
2 points
Question 6
1.
Determine if the function is a solution to the given differential e
quation.
y = x ln x - 4x + 5; yʹʹ - = 0.
Yes
No
2 points
Question 7
1.
Evaluate using integration by parts.

5. (x2 - x) ln (16x) - + 2x + C
(x2 - x) ln (16x) - + x + C
ln (16x) - + x + C
(x2 - x) ln (16x) - x2 + x + C
2 points
Question 8
1.
Find the general solution for the differential equation.
= 4P
P = 4eCt
P = Ce4t
P = Ce-4t

6. P = Cet
2 points
Question 9
1.
Evaluate. Assume u > 0 when ln u appears.
dt
e-7t2 + C
- e-7t2 + C
e-7t2 + C
- e-7t2 + C
2 points
Question 10
1.
Find the general solution for the differential equation.

7. y ' = 72x2 - 20x
72x3 - 20x2 + C
24x3 - 20x2 + C
72x3 - 10x2 + C
24x3 - 10x2 + C
2 points
Question 11
1.
Find the general solution for the differential equation.
y ' = x - 16
2x2 - 16 + C
- 16x + C
- x + C

8. x3 - 16x + C
2 points
Question 12
1.
Evaluate using integration by parts.
e4xdx
(x - 8) e4x - e4x + C
(x - 8) e4x + e4x + C
4(x - 8) e4x - 16 e4x + C
(x - 8) e4x - e4x + C
2 points
Question 13
1.
Evaluate using integration by parts.

9. dx
5x(2x + 3)1/2 + (2x + 3)3/2 + C
5x(2x + 3)1/2 - (2x + 3)3/2 + C
x(2x + 3)1/2 - (2x + 3)3/2 + C
5x(2x + 3)1/2 - (2x + 3)3/2 + C
2 points
Question 14
1.
Write the first four elements of the sequence.
n
0, 2, ,
2, , ,
1, , ,

10. 0, 1, ,
2 points
Question 15
1.
Evaluate. Assume u > 0 when ln u appears.
dx
+ C
+ C
+ C
(ln 6x)2 + C
2 points
Question 16
1.
Evaluate. Assume u > 0 when ln u appears.

11. dp
e5p2+ C
- e5p2 + C
7e5p2 + C
-7e5p2 + C
2 points
Question 17
1.
Evaluate. Assume u > 0 when ln u appears.
dy
ln + C
18 ln + C
19 ln + C

12. ln + C
2 points
Question 18
1.
Evaluate using integration by parts.
dx
x(ln 2x)2 - 2 ln (2x) + C
ln (2x)2 - 2x ln (2x) - 2x + C
x(ln 2x)2 + 2x ln (2x) + 2x + C
x(ln 2x)2 - 2x ln (2x) + 2x + C
2 points
Question 19
1.
Evaluate using integration by parts.

13. ln x dx
x2ln x - x2 + C
ln x - x2 + C
x2ln x - x2 + 5x + C
x2ln x - x2 - 5x + C
2 points
Question 20
1.
Find the general solution for the differential equation.
y ' = 2e3x
2e3x + C
e3x + C
6e3x + C

14. e3x + C
2 points
Question 21
1.
Determine if the function is a solution to the given differential e
quation.
y = ex + 3xex; yʹʹ - 2yʹ + y = 0.
Yes
No
2 points
Question 22
1.
Evaluate. Assume u > 0 when ln u appears.
- (7x2 + 3)-6 + C

15. - (7x2 + 3)-6 + C
- (7x2 + 3)-4 + C
- (7x2 + 3)-4 + C
2 points
Question 23
1.
Evaluate. Assume u > 0 when ln u appears.
dy
- + C
- + C
+ C
+ C
2 points
Question 24

16. 1.
Find the general solution for the differential equation.
yʹ = - x4 + x6
y = -4 - 4x3 + 6x5 + C
y = 2 ln x - x6 + x8 + C
y = 2 ln x - x5 + x7 + C
y = - x4 + x6 + C
2 points
Question 25
1.
Determine if the function is a solution to the given differential e
quation.
y = 3e2x + xe2x; yʹʹ + 2yʹ + 1 = 0.
Yes

17. No
2 points
Question 26
1.
Find the particular solution determined by the given condition.
fʹ(x) = 3x2 - 2x; f(0) = 18
f(x) = 3x3 + 2x2 + 18
f(x) = x3 - x2 + 18
f(x) = x3 + 2x2 + 18
f(x) = 3x3 + x2 + 18
2 points
Question 27
1.
Evaluate using integration by parts.

18. x1 - n ln x + x1 - n + C
ln x - x1 - n + C
x1 - n ln x - x2 - n + C
x1 - n ln x - x1 - n + C
2 points
Question 28
1.
Evaluate using integration by parts.
ln 7x dx
x5 ln 7x - x5 + C
ln 7x - x5 + C
x5 ln 7x - x6 + C

19. x5 ln 7x + x5 + C
2 points
Question 29
1.
Evaluate. Assume u > 0 when ln u appears.
dx
-11 e-4x3 + C
12 e-4x3 + C
e-4x3 + C
- e-4x3 + C
2 points
Question 30
1.
Find the particular solution determined by the given condition.
fʹ(x) = x4/5 + x; f(1) = -6

20. f(x) = x1/5 + x2 -
f(x) = x9/5 + x2 -
f(x) = x9/5 - x2 +
f(x) = x9/5 + 2x2 +
2 points
Question 31
1.
Evaluate using integration by parts.
7x ln x - x + C
x ln 7x + x + C
x ln 7x - 7x + C
x ln 7x - x + C

21. 2 points
Question 32
1.
Evaluate using integration by parts.
- x e-5x - e-5x + C
-10x e-5x - 80 e-5x + C
x e-5x + e-5x + C
- x e-5x - e-5x + C
2 points
Question 33
1.
Determine if the function is a solution to the given differential e
quation.
y = 2e2x + xe2x; yʹʹ - 2yʹ + 1 = 0.

22. No
Yes
2 points
Question 34
1.
Evaluate. Assume u > 0 when ln u appears.
dx
+ C
(x5 - 4)5 + C
+ C
+ C
2 points
Question 35
1.

23. Evaluate. Assume u > 0 when ln u appears.
ln + C
20 ln + C
20 ln(4x5 + 8) + C
ln + C
2 points
Question 36
1.
Determine if the function is a solution to the given differential e
quation.
y = e-x + 2xe-x; yʹʹ + 2yʹ + y = 0.
No
Yes

24. 2 points
Question 37
1.
Find the general solution for the differential equation.
y ' - 12x2 = 20
- 4x3 + 20x + C
4x3 + 10x + C
4x3 + 20x + C
4x3 - 10x + C
2 points
Question 38
1.
Evaluate using integration by parts.
dx

25. x3/2 ln + x3/2 + C
x3/2 ln - x3/2 + C
x3/2 ln - x3/2 + C
5x3/2 ln - 5x3/2 + C
2 points
Question 39
1.
Find the particular solution determined by the given condition.
= 5H; where H = 6.5 when t = 0
H(t) = e5t + 6.5
H(t) = 5e6.5t
H(t) = 6.5e5t
H(t) = 6.5e5t + 6.5
2 points

26. Question 40
1.
Evaluate using integration by parts.
6ex - 6xex + C
6ex - ex + C
6xex - 6ex + C
xex - 6ex + C
2 points
Question 41
1.
Determine if the function is a solution to the given differential e
quation.
y = 4x ln x + 4x + 5; yʹʹ - = 0.

27. Yes
No
2 points
Question 42
1.
Evaluate using integration by parts.
dx
- x(3 - x)3/2 + (3 - x)5/2 + C
x(3 - x)3/2 + (3 - x)5/2 + C
- x(3 - x)3/2 - (3 - x)5/2 + C
- x(3 - x)3/2 - (3 - x)5/2 + C
2 points
Question 43
1.

28. Find the general solution for the differential equation.
= 7y
y = Cex
y = Ce-7x
y = Ce7x
y = 7eCx
2 points
Question 44
1.
Evaluate using integration by parts.
dx
x4(ln 4x)2 - 39x3 ln 4x + C
x4(ln 4x)2 + 39x4 ln 4x - x4 + C
x4(ln 4x)2 - x4 ln 4x + x4 + C

29. x4(ln 4x)2 - 39x4 ln 4x + x4 + C
2 points
Question 45
1.
Find the particular solution determined by the given condition.
= 0.24D; where D(0) = 200
D(t) = 200e0.24t
D(t) = 200e0.24t + 200
D(t) = e48t
D(t) = 0.24e200t
2 points
Question 46
1.
Evaluate using integration by parts.

30. dx
x2(x2 + 8)3/2 - (x2 + 8)5/2 + C
x2(x2 + 8)3/2 + (x2 + 8)5/2 + C
x(x2 + 8)3/2 - (x2 + 8)7/2 + C
2x2(x2 + 8)3/2 - 2(x2 + 8)5/2 + C
2 points
Question 47
1.
Evaluate using integration by parts.
dx
x(3x - 10)3/2 - (3x - 10)5/2 + C
x(3x - 10)3/2 - (3x - 10)5/2 + C

31. x(3x - 10)3/2 - (3x - 10)5/2 + C
x(3x - 10)3/2 + (3x - 10)5/2 + C
2 points
Question 48
1.
Find the general solution for the differential equation.
y ' = 18x2
x3 + C
6x3 + C
18x3 + C
+ C
2 points
Question 49
1.
Find the particular solution determined by the given condition.

32. yʹ = 4x + 10; y = -21 when x = 0
y = 4x2 + 10x - 10.5
y = 4x2 + 10x - 21
y = 2x2 + 10x - 10.5
y = 2x2 + 10x - 21
2 points
Question 50
1.
Evaluate using integration by parts.
dx
+ C
+ C
7ex(x + 1)2 + C

33. - - 7ex + C