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Byju's Answer
Standard XII
Mathematics
Integration of Trigonometric Functions
If ∫x4+1xx2+1...
Question
If
∫
x
4
+
1
x
(
x
2
+
1
)
2
d
x
=
A
ln
|
x
|
+
B
1
+
x
2
+
C
,
where
C
is the constant of integration, then
|
A
+
B
|
is equal to
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Solution
Let
I
=
∫
x
4
+
1
x
(
x
2
+
1
)
2
d
x
=
∫
(
x
2
+
1
)
2
−
2
x
2
x
(
x
2
+
1
)
2
d
x
=
∫
1
x
d
x
−
∫
2
x
(
x
2
+
1
)
2
d
x
=
ln
|
x
|
+
1
1
+
x
2
+
C
⇒
A
=
1
,
B
=
1
∴
|
A
+
B
|
=
2
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