Test:
Integration IV - Ambitious
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Question 1:
Determine the integral:
∫
(
3
x
+
4
)
2
d
x
A
(
x
+
4
)
3
3
+
C
B
(
3
x
+
4
)
2
6
+
C
C
(
3
x
+
4
)
3
9
+
C
D
(
3
x
+
4
)
3
+
C
Question 2:
Determine the integral:
∫
(
4
+
3
x
)
−
6
d
x
A
(
1
+
3
x
)
−
5
3
+
C
B
(
4
−
1
x
)
−
5
4
+
C
C
−
(
4
+
3
x
)
−
5
15
+
C
D
−
(
4
−
3
x
)
−
5
6
+
C
Question 3:
Determine the integral:
∫
5
cos
(
3
x
−
1
)
d
x
A
−
5
3
cos
(
3
x
−
1
)
+
C
B
5
3
sin
(
3
x
−
1
)
+
C
C
3
sin
(
3
x
−
1
)
+
C
D
−
5
sin
(
3
x
−
1
)
+
C
Question 4:
Determine the integral:
∫
3
4
x
+
5
d
x
A
3
4
x
+
5
4
ln
3
+
C
B
3
4
x
+
5
ln
3
+
C
C
3
4
x
+
5
ln
4
+
C
D
e
4
x
+
5
+
C
Question 5:
Determine the integral:
∫
12
e
2
−
7
x
d
x
A
(
2
−
7
x
)
e
2
−
7
x
+
C
B
−
144
e
2
−
7
x
+
C
C
−
12
7
e
2
−
7
x
+
C
D
e
2
−
7
x
+
C
Question 6:
Determine the integral:
∫
8
x
−
28
x
2
−
6
x
+
8
d
x
A
−
2
ln
(
x
−
2
)
+
7
ln
(
x
−
4
)
+
C
B
8
ln
(
x
−
6
)
+
C
C
6
ln
(
x
−
2
)
+
2
ln
(
x
−
4
)
+
C
D
8
ln
(
x
−
1
)
+
4
ln
(
x
−
2
)
+
C
Question 7:
Determine the integral:
∫
2
x
2
+
18
x
+
31
x
2
+
5
x
+
6
d
x
A
2
x
+
3
ln
(
x
+
2
)
+
5
ln
(
x
+
3
)
+
C
B
6
ln
(
x
−
2
)
+
5
ln
(
x
−
3
)
+
C
C
−
3
x
+
2
ln
(
x
+
2
)
−
7
ln
(
x
+
3
)
+
C
D
x
−
4
ln
(
x
+
2
)
−
3
ln
(
x
+
5
)
+
C
Question 8:
Determine the integral:
∫
1
3
2
x
5
d
x
A
484
B
242
2
3
C
2
D
486
Question 9:
Determine the integral:
∫
0
π
(
cos
x
−
sin
x
)
d
x
A
−
1
B
1
C
0
D
2
Question 10:
Find the area bounded by the curve
y
=
5
x
2
+
7
x
+
1
and
x
-axis between
x
=
−
1
and
x
=
1
A
6
u
n
i
t
s
B
5
1
3
u
n
i
t
s
C
5
2
3
u
n
i
t
s
D
5
u
n
i
t
s
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