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