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Mathematics
Mathematics
Problem
a. (i) Write the partial fraction decomposition of
4
x
+
1
(
x
−
2
)
2
(
x
+
1
)
\displaystyle\frac{4x+1}{(x-2)^2(x+1)}
(
x
−
2
)
2
(
x
+
1
)
4
x
+
1
. b. (ii) Hence evaluate
∫
4
x
+
1
(
x
−
2
)
2
(
x
+
1
)
d
x
\displaystyle\int \frac{4x+1}{(x-2)^2(x+1)}\,dx
∫
(
x
−
2
)
2
(
x
+
1
)
4
x
+
1
d
x
.
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