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Mathematics
Problem
Evaluate
∫
x
3
+
2
x
2
−
5
x
+
3
x
+
1
d
x
\displaystyle \int \frac{x^{3}+2x^{2}-5x+3}{x+1}\,dx
∫
x
+
1
x
3
+
2
x
2
−
5
x
+
3
d
x
. a)
x
3
3
+
x
2
2
−
6
x
+
9
ln
∣
x
+
1
∣
+
C
\dfrac{x^{3}}{3}+\dfrac{x^{2}}{2}-6x+9\ln|x+1|+C
3
x
3
+
2
x
2
−
6
x
+
9
ln
∣
x
+
1∣
+
C
b)
x
3
3
+
x
2
2
−
6
x
+
ln
∣
x
+
1
∣
+
C
\dfrac{x^{3}}{3}+\dfrac{x^{2}}{2}-6x+\ln|x+1|+C
3
x
3
+
2
x
2
−
6
x
+
ln
∣
x
+
1∣
+
C
c)
x
3
3
+
x
2
2
−
6
x
−
9
ln
∣
x
+
1
∣
+
C
\dfrac{x^{3}}{3}+\dfrac{x^{2}}{2}-6x-9\ln|x+1|+C
3
x
3
+
2
x
2
−
6
x
−
9
ln
∣
x
+
1∣
+
C
d)
x
3
3
+
x
2
2
−
6
x
+
9
(
x
+
1
)
+
C
\dfrac{x^{3}}{3}+\dfrac{x^{2}}{2}-6x+9(x+1)+C
3
x
3
+
2
x
2
−
6
x
+
9
(
x
+
1
)
+
C
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