The improper integral depends on the real parameter

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

Problem

The improper integral

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

depends on the real parameter

p

. For which values of

p

does the integral converge? (a)

p\ge 1

(b)

0<p<1

(c)

p>1

(d) All real

p