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JEE Main Math Class 12 Integrals Part 1 Questions
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© examsnet.com
Question : 3
Total: 100
If
∫
tan
x
1
+
tan
x
+
tan
2
x
d
x
=
x
−
K
√
A
tan
−
1
(
K
tan
x
+
1
√
A
)
+
C
,
(
C
is a constant of integration), then the ordered pair
(
K
,
A
)
is euqal to
[Online April 16, 2018]
(2,3)
(2,1)
(-2,1)
(-2,3)
Validate
Solution:
Let
I
=
∫
tan
x
1
+
tan
x
+
tan
2
x
d
x
⇒
I
=
∫
tan
x
+
1
+
tan
2
x
tan
x
+
1
+
tan
2
x
d
x
−
∫
(
1
+
tan
2
x
)
1
+
tan
x
+
tan
2
x
⇒
I
=
x
−
∫
sec
2
x
d
x
1
+
tan
x
+
tan
2
x
Put
tan
x
=
t
⇒
sec
2
x
.
d
x
=
d
t
∴
I
=
x
−
∫
d
t
t
2
+
t
+
1
4
+
1
−
1
4
=
x
−
∫
d
t
(
t
+
1
2
)
2
+
(
√
3
2
)
2
⇒
I
=
x
−
2
√
3
tan
−
1
(
t
+
1
2
√
3
2
)
+
C
⇒
I
=
x
−
2
√
3
tan
−
1
(
2
tan
x
+
1
√
3
)
+
C
∴
A
=
3
and
K
=
2
© examsnet.com
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