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Mathematics
Problem
Find the value of
∫
2
x
2
+
3
x
+
1
x
(
x
+
1
)
(
x
+
2
)
d
x
\displaystyle \int \frac{2x^{2}+3x+1}{x(x+1)(x+2)}\,dx
∫
x
(
x
+
1
)
(
x
+
2
)
2
x
2
+
3
x
+
1
d
x
. a)
1
2
ln
∣
x
∣
+
3
2
ln
∣
x
+
1
∣
+
C
\dfrac{1}{2}\ln|x|+\dfrac{3}{2}\ln|x+1|+C
2
1
ln
∣
x
∣
+
2
3
ln
∣
x
+
1∣
+
C
b)
ln
∣
x
∣
+
3
2
ln
∣
x
+
2
∣
+
C
\ln|x|+\dfrac{3}{2}\ln|x+2|+C
ln
∣
x
∣
+
2
3
ln
∣
x
+
2∣
+
C
c)
1
2
ln
∣
x
∣
+
3
2
ln
∣
x
+
2
∣
+
C
\dfrac{1}{2}\ln|x|+\dfrac{3}{2}\ln|x+2|+C
2
1
ln
∣
x
∣
+
2
3
ln
∣
x
+
2∣
+
C
d)
1
2
ln
∣
x
∣
+
3
2
ln
∣
x
+
2
∣
−
ln
∣
x
+
1
∣
+
C
\dfrac{1}{2}\ln|x|+\dfrac{3}{2}\ln|x+2|-\ln|x+1|+C
2
1
ln
∣
x
∣
+
2
3
ln
∣
x
+
2∣
−
ln
∣
x
+
1∣
+
C
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