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Byju's Answer
Standard XII
Mathematics
Theorems on Integration
Evaluate : ∫...
Question
Evaluate :
∫
[
√
t
a
n
x
+
√
c
o
t
x
]
d
x
.
Open in App
Solution
I
=
∫
(
√
tan
x
+
√
cot
x
)
d
x
∴
I
=
∫
√
sin
x
cos
x
+
√
cos
x
sin
x
d
x
∴
I
=
∫
sin
x
+
cos
x
√
sin
x
cos
x
d
x
sin
x
−
cos
x
=
t
∴
(
cos
x
+
sin
x
)
d
x
=
d
t
∴
1
−
2
sin
x
cos
x
=
t
2
∴
I
=
∫
√
2
√
1
−
t
2
d
t
∴
I
=
√
2
sin
−
1
t
+
c
∴
I
=
√
2
sin
−
1
(
sin
x
−
cos
x
)
+
c
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