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KEAM 2019 Math Paper
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© examsnet.com
Question : 11
Total: 121
∫
cos
{
2
tan
−
1
√
1
−
x
1
+
x
}
d
x
is equal to
1
2
x
2
+
k
1
2
x
+
k
1
4
(
x
2
+
1
)
+
k
x
2
+
k
None of these
Validate
Solution:
Let
I
=
∫
cos
{
2
tan
−
1
√
1
−
x
1
+
x
}
d
x
Put,
x
=
cos
2
θ
I
=
∫
cos
{
2
tan
−
1
tan
θ
}
(
−
2
sin
2
θ
)
d
θ
=
−
∫
sin
4
θ
d
θ
=
1
4
cos
4
θ
+
C
=
1
4
(
2
x
2
−
1
)
+
C
=
1
2
x
2
+
k
© examsnet.com
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