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NDA Math Indefinite Integrals
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© examsnet.com
Question : 33
Total: 38
What is
∫
d
x
√
x
2
+
a
2
equal to ?
where c is the constant of integration.
[NDA I 2015]
l
n
|
x
+
√
x
2
+
a
2
a
|
+
c
l
n
|
x
−
√
x
2
+
a
2
a
|
+
c
l
n
|
x
2
+
√
x
2
+
a
2
a
|
+
c
None of the above
Validate
Solution:
Consider the given indefinite integral. It can be solved in the following way.
I
=
∫
d
x
√
x
2
+
a
2
Let
x
=
a
t
a
n
θ
d
x
=
a
s
e
c
2
θ
d
θ
I
=
∫
d
x
√
x
2
+
a
2
=
∫
a
s
e
c
2
θ
d
θ
√
a
2
(
tan
2
θ
+
1
)
=
∫
a
s
e
c
2
θ
d
θ
a
s
e
c
θ
=
∫
s
e
c
θ
d
θ
=
l
n
|
s
e
c
θ
+
t
a
n
θ
|
=
l
n
|
√
x
2
+
a
2
+
x
a
|
I
=
l
n
|
√
x
2
+
a
2
+
x
a
|
+
C
© examsnet.com
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