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Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus Name___________________________________
Period____Date________________
Integration by Substitution
Evaluate each indefinite integral. Use the provided substitution.
1)
∫
−15
x
4
(
−3
x
5
− 1
)
5
dx;
u =
−3
x
5
− 1 2)
∫
−16
x
3
(
−4
x
4
− 1
)
−5
dx;
u =
−4
x
4
− 1
3)
∫
−
8
x
3
(
−2
x
4
+ 5
)
5
dx;
u =
−2
x
4
+ 5
4)
∫
(
5
x
4
+ 5
)
2
3
⋅ 20
x
3
dx;
u =
5
x
4
+ 5
5)
∫
(
5 + ln
x
)
5
x
dx;
u =
5 + ln
x
6)
∫
4sec
4
x ⋅ tan
4
x ⋅
sec
4
4
x
dx;
u = sec
4
x
7)
∫
36
x
3
(
3
x
4
+ 3
)
5
dx;
u =
3
x
4
+ 3 8)
∫
x
(
4
x − 1
)
4
dx;
u =
4
x − 1
-1-
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Worksheet by Kuta Software LLC
Evaluate each indefinite integral.
9)
∫
−9
x
2
(
−3
x
3
+ 1
)
3
dx 10)
∫
12
x
3
(
3
x
4
+ 4
)
4
dx
11)
∫
−12
x
2
(
−4
x
3
+ 2
)
−3
dx
12)
∫
(
3
x
5
− 3
)
3
5
⋅ 15
x
4
dx
13)
∫
(
−2
x
4
− 4
)
4
⋅ −32
x
3
dx
14)
∫
(
e
4
x
− 4
)
1
5
⋅
8
e
4
x
dx
15)
∫
x
(
4
x + 5
)
3
dx 16)
∫
5
x
2
x + 3
dx
-2-
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus Name___________________________________
Period____Date________________
Integration by Substitution
Evaluate each indefinite integral. Use the provided substitution.
1)
∫
−15
x
4
(
−3
x
5
− 1
)
5
dx;
u =
−3
x
5
− 1
1
6
(
−3
x
5
− 1
)
6
+
C
2)
∫
−16
x
3
(
−4
x
4
− 1
)
−5
dx;
u =
−4
x
4
− 1
−
1
4
(
−4
x
4
− 1
)
4
+
C
3)
∫
−
8
x
3
(
−2
x
4
+ 5
)
5
dx;
u =
−2
x
4
+ 5
−
1
4
(
−2
x
4
+ 5
)
4
+
C
4)
∫
(
5
x
4
+ 5
)
2
3
⋅ 20
x
3
dx;
u =
5
x
4
+ 5
3
5
(
5
x
4
+ 5
)
5
3
+
C
5)
∫
(
5 + ln
x
)
5
x
dx;
u =
5 + ln
x
1
6
(
5 + ln
x
)
6
+
C
6)
∫
4sec
4
x ⋅ tan
4
x ⋅
sec
4
4
x
dx;
u = sec
4
x
1
5
⋅
sec
5
4
x +
C
7)
∫
36
x
3
(
3
x
4
+ 3
)
5
dx;
u =
3
x
4
+ 3
1
2
(
3
x
4
+ 3
)
6
+
C
8)
∫
x
(
4
x − 1
)
4
dx;
u =
4
x − 1
1
96
(
4
x − 1
)
6
+
1
80
(
4
x − 1
)
5
+
C
-1-
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Worksheet by Kuta Software LLC
Evaluate each indefinite integral.
9)
∫
−9
x
2
(
−3
x
3
+ 1
)
3
dx
1
4
(
−3
x
3
+ 1
)
4
+
C
10)
∫
12
x
3
(
3
x
4
+ 4
)
4
dx
1
5
(
3
x
4
+ 4
)
5
+
C
11)
∫
−12
x
2
(
−4
x
3
+ 2
)
−3
dx
−
1
2
(
−4
x
3
+ 2
)
2
+
C
12)
∫
(
3
x
5
− 3
)
3
5
⋅ 15
x
4
dx
5
8
(
3
x
5
− 3
)
8
5
+
C
13)
∫
(
−2
x
4
− 4
)
4
⋅ −32
x
3
dx
4
5
(
−2
x
4
− 4
)
5
+
C
14)
∫
(
e
4
x
− 4
)
1
5
⋅
8
e
4
x
dx
5
3
(
e
4
x
− 4
)
6
5
+
C
15)
∫
x
(
4
x + 5
)
3
dx
1
80
(
4
x + 5
)
5
−
5
64
(
4
x + 5
)
4
+
C
16)
∫
5
x
2
x + 3
dx
1
2
(
2
x + 3
)
5
2
−
5
2
(
2
x + 3
)
3
2
+
C
-2-
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