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Byju's Answer
Standard XI
Mathematics
Integration by Parts
Let gx = ∫1 +...
Question
Let
g
(
x
)
=
∫
1
+
2
cos
x
(
cos
x
+
2
)
2
d
x
and
g
(
0
)
=
0
, the value of
8
g
(
π
2
)
is
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Solution
g
(
x
)
=
∫
cos
x
(
cos
x
+
2
)
+
sin
2
x
(
cos
x
+
2
)
2
d
x
=
∫
cos
x
I
I
.
1
cos
x
+
2
I
d
x
+
∫
sin
2
x
(
cos
x
+
2
)
2
d
x
=
1
cos
x
+
2
sin
x
−
∫
sin
2
x
(
cos
x
+
2
)
2
d
x
+
∫
sin
2
x
(
cos
x
+
2
)
2
d
x
∴
g
(
x
)
=
sin
x
cos
x
+
2
+
c
g
(
0
)
=
0
⇒
c
=
0
∴
g
(
x
)
=
sin
x
cos
x
+
2
⇒
g
(
π
2
)
=
1
2
∴
8
g
(
π
2
)
=
4
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Standard XI Mathematics
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