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Byju's Answer
Standard XII
Mathematics
Standard Formulae - 1
∫sin5 x/2/sin...
Question
∫
sin
5
x
2
sin
x
2
d
x
is equal to:
(where
c
is a constant of integration.)
A
x
+
2
sin
x
+
sin
2
x
+
c
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B
x
+
2
sin
x
+
2
sin
2
x
+
c
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C
2
x
+
sin
x
+
sin
2
x
+
c
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D
2
x
+
sin
x
+
2
sin
2
x
+
c
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Solution
The correct option is
A
x
+
2
sin
x
+
sin
2
x
+
c
I
=
∫
sin
5
x
2
sin
x
2
d
x
=
∫
2
sin
5
x
2
cos
x
2
sin
x
d
x
=
∫
sin
3
x
+
sin
2
x
sin
x
d
x
=
∫
(
3
sin
x
−
4
sin
3
x
)
+
2
sin
x
cos
x
sin
x
d
x
=
∫
(
3
−
4
sin
2
x
+
2
cos
x
)
d
x
=
∫
(
3
−
2
(
1
−
cos
2
x
)
+
2
cos
x
)
d
x
=
∫
(
3
−
2
+
2
cos
2
x
+
2
cos
x
)
d
x
=
∫
(
1
+
2
cos
2
x
+
2
cos
x
)
d
x
=
x
+
sin
2
x
+
2
sin
x
+
c
Suggest Corrections
7
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(where
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