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JEE Main Math Class 12 Integrals Part 1 Questions
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© examsnet.com
Question : 20
Total: 100
The integral
∫
2
x
12
+
5
x
9
(
x
5
+
x
3
+
1
)
3
d
x
is equal to:
[2016]
x
5
2
(
x
5
+
x
3
+
1
)
2
+
C
−
x
10
2
(
x
5
+
x
3
+
1
)
2
+
C
−
x
5
(
x
5
+
x
3
+
1
)
2
+
C
x
10
2
(
x
5
+
x
3
+
1
)
2
+
C
Validate
Solution:
∫
2
x
12
+
5
x
9
(
x
5
+
x
3
+
1
)
3
d
x
Dividing by
x
15
in numerator and denominator
∫
2
x
3
+
5
x
6
d
x
(
1
+
1
x
2
+
1
x
5
)
3
Let
1
+
1
x
2
+
1
x
5
=
t
⇒
(
−
2
x
3
−
5
x
6
)
d
x
=
d
t
⇒
(
2
x
3
+
5
x
6
)
d
x
=
−
d
t
This gives,
∫
2
x
3
+
5
x
6
d
x
(
1
+
1
x
2
+
1
x
5
)
3
=
∫
−
d
t
t
3
=
1
2
t
2
+
C
=
1
2
(
1
+
1
x
2
+
1
x
5
)
2
+
C
=
x
10
2
(
x
5
+
x
3
+
1
)
2
+
C
© examsnet.com
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