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Mathematics
Mathematics
Problem
To test the convergence of
∫
1
∞
x
x
3
+
1
d
x
\displaystyle \int_{1}^{\infty} \frac{\sqrt{x}}{x^{3}+1}\,dx
∫
1
∞
x
3
+
1
x
d
x
, which of the following comparison functions is most appropriate? a)
1
x
3
/
2
\dfrac{1}{x^{3/2}}
x
3/2
1
b)
1
x
5
/
2
\dfrac{1}{x^{5/2}}
x
5/2
1
c)
1
x
\dfrac{1}{x}
x
1
d)
1
x
\dfrac{1}{\sqrt{x}}
x
1
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