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Mathematics
Problem
Find
∫
x
2
+
3
x
+
5
x
+
1
d
x
\displaystyle\int \frac{x^{2}+3x+5}{x+1}\,dx
∫
x
+
1
x
2
+
3
x
+
5
d
x
. a)
1
2
x
2
+
2
x
+
ln
∣
x
+
1
∣
+
C
\dfrac12 x^{2}+2x+\ln|x+1|+C
2
1
x
2
+
2
x
+
ln
∣
x
+
1∣
+
C
b)
1
2
x
2
+
2
x
+
3
ln
∣
x
+
1
∣
+
C
\dfrac12 x^{2}+2x+3\ln|x+1|+C
2
1
x
2
+
2
x
+
3
ln
∣
x
+
1∣
+
C
c)
1
2
x
2
+
2
x
+
3
ln
∣
x
∣
+
C
\dfrac12 x^{2}+2x+3\ln|x|+C
2
1
x
2
+
2
x
+
3
ln
∣
x
∣
+
C
d)
x
2
+
2
x
+
3
ln
∣
x
+
1
∣
+
C
x^{2}+2x+3\ln|x+1|+C
x
2
+
2
x
+
3
ln
∣
x
+
1∣
+
C
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