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Mathematics
Mathematics
Problem
∫
[
tan
x
+
cot
x
]
d
x
\int [\sqrt{\tan x} + \sqrt{\cot x}] dx
∫
[
tan
x
+
cot
x
]
d
x
is equal to (a)
2
tan
−
1
(
tan
x
2
tan
x
)
+
c
\sqrt{2} \tan^{-1} \left( \frac{\tan x}{\sqrt{2 \tan x}} \right) + c
2
tan
−
1
(
2
t
a
n
x
t
a
n
x
)
+
c
(b)
2
tan
−
1
(
tan
x
−
1
2
tan
x
)
+
c
\sqrt{2} \tan^{-1} \left( \frac{\tan x - 1}{\sqrt{2 \tan x}} \right) + c
2
tan
−
1
(
2
t
a
n
x
t
a
n
x
−
1
)
+
c
(c)
tan
x
2
tan
−
1
(
cot
x
+
1
2
tan
x
)
+
c
\frac{\tan x}{\sqrt{2}} \tan^{-1} \left( \frac{\cot x + 1}{\sqrt{2 \tan x}} \right) + c
2
t
a
n
x
tan
−
1
(
2
t
a
n
x
c
o
t
x
+
1
)
+
c
(d)
tan
x
2
tan
−
1
(
cot
x
−
1
2
cot
x
)
+
c
\frac{\tan x}{\sqrt{2}} \tan^{-1} \left( \frac{\cot x - 1}{\sqrt{2 \cot x}} \right) + c
2
t
a
n
x
tan
−
1
(
2
c
o
t
x
c
o
t
x
−
1
)
+
c
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