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JEE Main Math Class 12 Integrals Part 1 Questions
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© examsnet.com
Question : 2
Total: 100
The integral
∫
sin
2
x
cos
2
x
(
sin
5
x
+
cos
3
x
sin
2
x
+
sin
3
x
cos
2
x
+
cos
5
x
)
2
d
x
is equal to:
[2018]
−
1
3
(
1
+
tan
3
x
)
+
C
1
1
+
cot
3
x
+
C
−
1
1
+
cot
3
x
+
C
1
3
(
1
+
tan
3
x
)
+
C
Validate
Solution:
Let I
∫
sin
2
x
cos
2
x
(
sin
5
x
+
cos
3
x
sin
2
x
+
sin
3
x
cos
2
x
+
cos
5
x
)
2
d
x
=
∫
sin
2
x
cos
2
x
[
(
sin
2
x
+
cos
2
x
)
(
sin
3
x
+
cos
3
x
)
]
2
d
x
=
∫
sin
2
x
cos
2
x
(
sin
3
x
+
cos
3
x
)
2
d
x
=
∫
tan
2
x
.
sec
2
x
(
1
+
tan
3
x
)
2
d
x
Now, put
(
1
+
tan
3
x
)
=
t
⇒
3
tan
2
x
sec
2
x
d
x
=
d
t
∴
I
=
1
3
∫
d
t
t
2
=
−
1
3
t
+
C
=
−
1
3
(
1
+
tan
3
x
)
+
C
© examsnet.com
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