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EXAMPLE 3
Using Properties of the Indefinite Integral
(a)
∫
(
12
x
5
+
1
√
x
)
d
x
=
12
∫
1
x
5
d
x
+
∫
1
√
x
d
x
=
12
∫
x
−
5
d
x
+
∫
x
−
1
/
2
d
x
=
12
(
x
−
4
−
4
)
+
x
1
/
2
1
2
+
C
=
−
3
x
4
+
2
√
x
+
C
(b)
∫
x
2
+
6
x
2
+
1
d
x
=
↑
Algebra
∫
(
x
2
+
1
)
+
5
x
2
+
1
d
x
=
∫
[
x
2
+
1
x
2
+
1
+
5
x
2
+
1
]
d
x
=
∫
[
1
+
5
x
2
+
1
]
d
x
=
↑
Sum Property
∫
d
x
+
∫
5
x
2
+
1
d
x
=
∫
d
x
+
5
∫
1
x
2
+
1
d
x
=
x
+
5
tan
−
1
x
+
C
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