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NDA Math Indefinite Integrals
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© examsnet.com
Question : 11
Total: 38
What is
∫
d
x
sec
2
(
tan
−
1
x
)
equal to?
[NDA-I 2021]
sin
−
1
x
+
c
tan
−
1
x
+
c
sec
−
1
x
+
c
cos
−
1
x
+
c
Validate
Solution:
👈: Video Solution
CONCEPT:
-
sec
2
x
−
tan
2
x
=
1
-
∫
d
x
1
+
x
2
=
tan
−
1
x
+
C
where
C
is a constant
CALCULATION:
Let
I
=
∫
d
x
sec
2
(
tan
−
1
x
)
As we know that,
sec
2
x
−
tan
2
x
=
1
⇒
I
=
∫
d
x
1
+
tan
2
(
tan
−
1
x
)
⇒
I
=
∫
d
x
1
+
[
tan
(
tan
−
1
x
)
]
2
⇒
I
=
∫
d
x
1
+
x
2
As we know that,
∫
d
x
1
+
x
2
=
tan
−
1
x
+
C
where
C
is constant.
⇒
I
=
∫
d
x
sec
2
(
tan
−
1
x
)
=
tan
−
1
x
+
C
Hence, option 2 is correct.
© examsnet.com
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