p
x
2
1
3
+C
C)e
5x
p
x
2
p
x
2
5x
+C
D)e
15x+14
D) 3x2
arctan (x) + C
Math 1431
LAB session 17
sin (x) + C
Quiz 26
C) 3x2
15x+C
2
Example 1:
Z
p
Z
15x+34
5x + 4 dx
6x
dx
(x2 + 5)3
Z
5x
2
p
3
x3 + 8 dx
5
D) 6x5 + 5x + C
C)6x5 + 5x + C
5x + C
Z
2
8x + 325x2 1
C) 2 +dx
+C
x
2
x + 8x 15
1
+p
+C
x
p
x
2
ex
+C
C)e5x
p
x
2
2
D) 3x2 +
+C
1
x2
D)e5x
+C
p
x
2
18
B) 13 arctan (x) + C
rcsin (x) + C
x2
2
15x+C
C) 3x2
2
Z
p
5x +2:4 dx
Example
Z
Z
Z
6x
dx
(x2 + 5)3
5x
p
2
p
3
x3 + 8 dx
8x + 32
dx
x2 + 8x 15
18
15x+14
2
D) 3x2
15x+34
Z
6x
dx
2
3
(x +3:5)
Example
Z
p
2 3 3
5x x + 8 dx
5
+ 5x + C C)6x5 + 5x + C D) 6x5 + 5x + C
Z
8x + 32 2
x2 p
1
5x dx 1
3x2
1
+
+
C
C)
+
+
C
D)
+
+C
2
2
xx + 8x
2
x
2
x2
15
B)e
p
x
2
x
+ C C)e
18
B) 13 arctan (x) + C
5x
p
x
2
5x
+C
D)e
15x+14
D) 3x2
p
x
2
arcsin (x) + C
) 3x2
2
15x+C
Z
Z
Z
p
2
5x + 4 dx
6x
dx
(x2 + 5)3
5x
2
p
3
Example 4:
Z
C) 3x2
p
x3 + 8 dx
8x + 32
dx
2
x + 8x 15
18
2
15x+34
Z
Example 5:
Z
1
p
2
6x xZ
0
Z
1)2 dx
p
a2 dx
cos (8x
4) dx
a
6x x2
0
1)2Zdx
7x2 (5x3
a
7x2 (5x3
1
Z
0
Z
0
a2 dx
sec (5x + 4) tan (5x + 4) dx
cos (8x
4)Zdx
sin3 (x) cos (x) dx
ec (5x + 4) tan (5x + 4)
dx
Z
Z 0
5x2
Z
2
3
2
xe
dx
7x (5x
1) dx
sin13 (x) cos (x) dx
Z
Z a p
ex
Z
2
p
dx
6x 5xx
a2 dx
2
2x
1 16e
dx
0 xe
Z
Z
cosex(8x 4) dx
p
dx
2x
Question
#
1 16e
Z
2 tan (5x + 4) dx
sec (5x +
7x4)
dx
3 + 1)2
(x
Z
Z 1 sin3 (x) cos (x) dx
6x5 (3x8 2)2 dx
0
Z
Z a p xe5x2 dx
5x a2 x2 dx
0 Z
ex
Z
p
dx
2x
1 tan16e
sec2 (3x)
(3x)
dx
Z
2
7x
Z
dx
8x32
2
(x
+
1)
dx
Question #6
1 + 4x
Z 1
6x5 (3x8 2)2 dx
0
Z
Z
a
p
5x a2
x2 dx
0
sec2 (3x) tan (3x) dx
19
Z
8x2
dx
1 + 4x6
19
Z
0
7x2 (5x3
1)2 dx
p
6x x2
a2 dx
cos (8x
4) dx
Example
6:
1
Z
a
0
Z
sec (5x + 4) tan (5x + 4) dx
Z
sin3 (x) cos (x) dx
Z
Z
Z
2
xe5x dx
ex
p
dx
1 16e2x
0
7x2 (5x3
1)2 dx
p
6x x2
a2 dx
cos (8x
4) dx
1
Z
a
Example
7:
0
Z
ec (5x + 4) tan (5x + 4) dx
Z
Z
sin3 (x) cos (x) dx
Z
2
xe5x dx
ex
p
dx
1 16e2x
19
0
Z
cos (8x
4) dx
Example 8:
Z
sec (5x + 4) tan (5x + 4) dx
Z
sin3 (x) cos (x) dx
Z
Z
Z
2
xe5x dx
ex
p
dx
1 16e2x
0
7x2 (5x3
1)2 dx
p
6x x2
a2 dx
cos (8x
4) dx
1
Z
a
0
Z
sec (5x + 4) tan (5x + 4) dx
Example 9:
Z
Z
sin3 (x) cos (x) dx
Z
2
xe5x dx
ex
p
dx
2x
1 16e
19
Z
sin3 (x) cos (x) dx
Example 10:
Z
xe
5x2
dx
ex
dx
Zp0
2x
1 2 16e3
7x (5x
1)2 dx
1
Z
p
6x x2
a2 dx
cos (8x
4) dx
a
0
Z
ec (5x + 4) tan (5x + 4) dx
Z
sin3 (x) cos (x) dx
Z
xe
5x2
Example 11:
Z
dx
ex
p
dx
2x
1 16e
19
Z Z 1
8
2
6x5 (3x
dx+ 4) dx
sec (5x
+ 4) tan2)(5x
0Question
#
Z 0ZZa p
3 a
32
x22(x)
dx
sin
(x)
cos
7x25x
(5x
1)
dxdx
Z
Z
1 0
Z
5x2(3x) dx
sec2 p
(3x)2xe
tan
6x x
a2dx
dx
a
0
Z
8x2ex
dx
p
6 2x dx
1
+
4x
cos (8x
4) dx
1 16e
Z
7x2
dx
3 + 1)2
(x
c (5x + 4) tan (5x + 4) dx
Z 1
Z
6x5 (3x8 2)2 dx
Z
sin03 (x) cos (x) dx
Z
p
a
Z 5x19a2 x2 dx
Question
2
0
5x#
xe
dx
Z
sec2 (3x) tan (3x) dx
Z
Z
Z
ex
pZ
dx
22x
8x
1 16e
1 2+ 4x6
dx
7x
dx
3
2
(x + 1)
1
6x5 (3x8
2)2 dx
0
Z
a
p
5x a2 19x2 dx
0
sec2 (3x) tan (3x) dx
Question #
Z
8x2
dx
1 + 4x6
19