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Tardigrade
Question
Mathematics
∫ (tan (ln x) tan(ln (x/2))tan (ln 2)/x)dx=
Q.
∫
x
t
an
(
l
n
x
)
t
an
(
l
n
2
x
)
t
an
(
l
n
2
)
d
x
=
5819
203
Integrals
Report Error
A
l
n
(
sec
(
l
n
2
x
)
sec
(
l
n
x
)
)
+
C
38%
B
l
n
(
sec
l
n
x
)
+
C
25%
C
l
n
(
sec
l
n
(
2
x
)
x
t
an
(
l
n
x
)
)
+
C
12%
D
l
n
(
sec
(
l
n
2
x
)
x
t
an
(
l
n
2
)
sec
(
l
n
x
)
)
+
C
25%
Solution:
l
n
x
=
l
n
(
2
x
)
+
l
n
2
⇒
t
an
(
l
n
x
)
=
1
−
t
an
(
l
n
x
/2
)
t
an
(
l
n
2
)
t
an
(
l
n
x
/2
)
+
t
an
(
l
n
2
)
⇒
t
an
(
l
n
x
)
t
an
(
l
n
2
x
)
t
an
(
l
n
2
)
=
t
an
(
l
n
x
)
−
t
an
(
l
n
2
x
)
−
t
an
(
l
n
2
)
∴
I
=
∫
x
t
an
(
l
n
x
)
d
x
−
∫
x
t
an
(
l
n
x
/2
)
d
x
−
∫
x
t
an
(
l
n
2
)
d
x
=
l
n
sec
(
l
n
x
)
−
l
n
sec
(
l
n
2
x
)
−
t
an
(
l
n
2
)
l
n
x
=
l
n
{
sec
(
l
n
(
x
/2
)
)
x
t
an
l
n
2
sec
(
l
n
x
)
}
+
C