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UPSC NDA 2 2017 Mathematics Solved Paper
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© examsnet.com
Question : 67
Total: 120
What is
∫
tan
−
1
(
secx
+
tanx
)
d
x
equal to ?
[NDA II 2017]
π
x
4
+
x
2
4
+
c
π
x
2
+
x
2
4
+
c
π
x
4
+
π
x
2
4
+
c
π
x
4
−
x
2
4
+
c
Validate
Solution:
∫
tan
−
1
(
sec
x
+
tan
x
)
d
x
=
∫
tan
−
1
(
tan
(
π
4
+
x
2
)
)
d
x
∴
sec
x
+
tan
x
=
1
+
sin
x
cos
x
=
tan
(
π
4
+
x
2
)
=
∫
(
π
4
+
x
2
)
d
x
=
π
x
4
+
x
2
4
+
c
© examsnet.com
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