int ((2x+11)/√5x²+10x+29)dx
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Answer:
Explanation:
1
x
−
1
x
+
1
−
1
(
x
+
1
)
2
Explanation:
1
x
3
+
2
x
2
+
x
=
1
x
⋅
(
x
2
+
2
x
+
1
)
=
1
x
⋅
(
x
+
1
)
2
Hence,
1
x
3
+
2
x
2
+
x
=
A
x
+
B
x
+
1
+
C
(
x
+
1
)
2
After expanding denominator,
A
⋅
(
x
+
1
)
2
+
B
⋅
(
x
2
+
x
)
+
C
x
=
1
Set
x
=
−
1
,
−
C
=
1
, so
C
=
−
1
Set
x
=
0
,
A
=
1
Set
x
=
1
,
−
4
A
+
2
B
+
C
=
1
, so
B
=
−
1
Thus,
1
x
3
+
2
x
2
+
x
=
1
x
−
1
x
+
1
−
1
(
x
+
1
)
2
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