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Decompose into the form and find the values of and .
MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals
Problem
Decompose
2
x
2
+
5
x
+
1
(
x
−
2
)
3
\dfrac{2x^{2}+5x+1}{(x-2)^{3}}
(
x
−
2
)
3
2
x
2
+
5
x
+
1
into the form
A
x
−
2
+
B
(
x
−
2
)
2
+
C
(
x
−
2
)
3
\dfrac{A}{x-2}+\dfrac{B}{(x-2)^{2}}+\dfrac{C}{(x-2)^{3}}
x
−
2
A
+
(
x
−
2
)
2
B
+
(
x
−
2
)
3
C
and find the values of
A
,
B
,
A,\;B,
A
,
B
,
and
C
C
C
.
Related theory
Integration Techniques
Integration by partial fractions
Integrals
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