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WeBWorK assignment due : 02/03/2016 at 03:00am EST.
1.
(1 pt)
Find the derivative of
f
(
x
) =
?
x
2
+
1
+
C
to complete the
following integration formula:
R
dx
=
?
x
2
+
1
+
C
2.
(1 pt)
Using an uppercase ”C” for any arbitrary constants, ?nd the
general inde?nite integral
Z

3
3
?
xdx
Integral =
3.
(1 pt)
Using an uppercase ”C” for any arbitrary constants, ?nd the
general inde?nite integral
Z
(
5

t
)(
7
+
t
2
)
dt
Integral =
4.
(1 pt)
Using an uppercase ”C” for any arbitrary constants, ?nd the
general inde?nite integral
Z
±
2
x
2

5
+

8
x
2
+
1
²
dx
Integral =
5.
(1 pt)
Evaluate the integral
Z
9
1
5
x
+
4
?
x
dx
Integral =
6.
(1 pt)
Evaluate the following integral by making the given substi
tution:
Z
x
(
7
+
x
2
)
10
dx
,
u
=
7
+
x
2
Note: Any arbitrary constants used must be an uppercase
”C”.
7.
(1 pt)
Evaluate the following integral by making the given substi
tution:
Z
4
e
sin
(
x
)
cos
(
x
)
dx
,
u
=
sin
(
x
)
Note: Any arbitrary constants used must be an uppercase
”C”.
8.
(1 pt)
Evaluate the inde?nite integral
Z

7
x
4
?
x
+
2
dx
Note: Any arbitrary constants used must be an uppercase
”C”.
9.
(1 pt)
Evaluate the de?nite integral (if it exists)
Z
2
1

9
x
?
x

1
dx
If the integral does not exist, type ”DNE”.
10.
(1 pt)
Using an uppercase ”C” for any arbitrary constants, ?nd the
general inde?nite integral
Z
(

9
e
u
+
5sec
2
(
u
))
du
Integral =
Generated by the WeBWorK system c
±
WeBWorK Team, Department of Mathematics, University of Rochester
1
Answer