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Mathematics
Problem
Evaluate
∫
2
x
+
3
x
2
+
3
x
+
2
d
x
\displaystyle\int \frac{2x+3}{x^{2}+3x+2}\,dx
∫
x
2
+
3
x
+
2
2
x
+
3
d
x
. a)
1
2
(
ln
∣
x
+
1
∣
+
ln
∣
x
+
2
∣
)
+
C
\tfrac12\bigl(\ln|x+1|+\ln|x+2|\bigr)+C
2
1
(
ln
∣
x
+
1∣
+
ln
∣
x
+
2∣
)
+
C
b)
ln
∣
x
2
+
3
x
+
2
∣
+
C
\ln\bigl|x^{2}+3x+2\bigr|+C
ln
x
2
+
3
x
+
2
+
C
c)
ln
∣
x
+
1
∣
−
ln
∣
x
+
2
∣
+
C
\ln|x+1|-\ln|x+2|+C
ln
∣
x
+
1∣
−
ln
∣
x
+
2∣
+
C
d)
1
2
ln
∣
x
2
+
3
x
+
2
∣
+
C
\tfrac12\,\ln|x^{2}+3x+2|+C
2
1
ln
∣
x
2
+
3
x
+
2∣
+
C
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