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Byju's Answer
Standard XII
Mathematics
Parametric Differentiation
Integrate the...
Question
Integrate the function
tan
−
1
x
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Solution
Let
I
=
∫
1
⋅
tan
−
1
x
d
x
Taking
tan
−
1
as first function and 1 as second function and integrating by parts, we obtain
I
=
tan
−
1
x
∫
1
d
x
−
∫
{
(
d
d
x
tan
−
1
x
)
∫
1
⋅
d
x
}
d
x
=
tan
−
1
x
⋅
x
−
∫
1
1
+
x
2
⋅
x
d
x
=
x
tan
−
1
x
−
1
2
∫
2
x
1
+
x
2
d
x
=
x
tan
−
1
x
−
1
2
log
|
1
+
x
2
|
+
C
=
x
tan
−
1
x
−
1
2
log
(
1
+
x
2
)
+
C
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