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Mathematics
Problem
Which of the following integrals must first be rewritten by dividing the polynomials so that the degree of the numerator is less than that of the denominator? a)
∫
2
x
x
2
+
1
d
x
\displaystyle \int \frac{2x}{x^{2}+1}\,dx
∫
x
2
+
1
2
x
d
x
b)
∫
x
3
+
2
x
+
1
x
2
−
1
d
x
\displaystyle \int \frac{x^{3}+2x+1}{x^{2}-1}\,dx
∫
x
2
−
1
x
3
+
2
x
+
1
d
x
c)
∫
x
2
+
3
x
3
+
1
d
x
\displaystyle \int \frac{x^{2}+3}{x^{3}+1}\,dx
∫
x
3
+
1
x
2
+
3
d
x
d)
∫
x
+
1
x
2
+
4
d
x
\displaystyle \int \frac{x+1}{x^{2}+4}\,dx
∫
x
2
+
4
x
+
1
d
x
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