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Mathematics
Problem
Evaluate
∫
x
3
x
2
+
1
d
x
\displaystyle \int \frac{x^{3}}{x^{2}+1}\,dx
∫
x
2
+
1
x
3
d
x
. a)
x
2
2
+
1
2
ln
(
x
2
+
1
)
+
C
\dfrac{x^{2}}{2} + \dfrac{1}{2}\ln (x^{2}+1) + C
2
x
2
+
2
1
ln
(
x
2
+
1
)
+
C
b)
x
2
4
−
1
2
ln
(
x
2
+
1
)
+
C
\dfrac{x^{2}}{4} - \dfrac{1}{2}\ln (x^{2}+1) + C
4
x
2
−
2
1
ln
(
x
2
+
1
)
+
C
c)
x
2
2
−
1
2
ln
(
x
2
+
1
)
+
C
\dfrac{x^{2}}{2} - \dfrac{1}{2}\ln (x^{2}+1) + C
2
x
2
−
2
1
ln
(
x
2
+
1
)
+
C
d)
x
2
2
−
ln
(
x
2
+
1
)
+
C
\dfrac{x^{2}}{2} - \ln (x^{2}+1) + C
2
x
2
−
ln
(
x
2
+
1
)
+
C
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