To test the convergence of

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

\displaystyle \int_{1}^{\infty} \frac{\sqrt{x}}{x^{3}+1}\,dx

, which of the following comparison functions is most appropriate? (a)

\dfrac{1}{x^{3/2}}

(b)

\dfrac{1}{x^{5/2}}

(c)

\dfrac{1}{x}

(d)

\dfrac{1}{\sqrt{x}}