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Mathematics
Problem
Calculate
∫
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)
x
2
2
+
2
x
+
3
x
+
1
+
C
\displaystyle \frac{x^{2}}{2}+2x+\frac{3}{x+1}+C
2
x
2
+
2
x
+
x
+
1
3
+
C
b)
x
2
2
+
3
x
+
2
ln
∣
x
+
1
∣
+
C
\displaystyle \frac{x^{2}}{2}+3x+2\ln|x+1|+C
2
x
2
+
3
x
+
2
ln
∣
x
+
1∣
+
C
c)
x
2
2
+
2
x
+
3
ln
∣
x
+
1
∣
+
C
\displaystyle \frac{x^{2}}{2}+2x+3\ln|x+1|+C
2
x
2
+
2
x
+
3
ln
∣
x
+
1∣
+
C
d)
x
2
2
+
2
x
+
3
ln
∣
x
∣
+
C
\displaystyle \frac{x^{2}}{2}+2x+3\ln|x|+C
2
x
2
+
2
x
+
3
ln
∣
x
∣
+
C
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