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Mathematics
Mathematics
Problem
Evaluate
∫
x
3
+
4
x
2
+
5
x
+
3
(
x
+
1
)
(
x
+
2
)
d
x
\displaystyle \int \frac{x^{3}+4x^{2}+5x+3}{(x+1)(x+2)}\,dx
∫
(
x
+
1
)
(
x
+
2
)
x
3
+
4
x
2
+
5
x
+
3
d
x
. Express your answer in the form
P
(
x
)
+
A
ln
∣
x
+
1
∣
+
B
ln
∣
x
+
2
∣
P(x)+A\ln|x+1|+B\ln|x+2|
P
(
x
)
+
A
ln
∣
x
+
1∣
+
B
ln
∣
x
+
2∣
, where
P
(
x
)
P(x)
P
(
x
)
is a polynomial.
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