Mathematics

Problem

Consider the improper integral

\displaystyle\int_{0}^{3}\frac{1}{(x-1)^2}\,dx

. Which of the following is true? a) The integral diverges because the integrand has a vertical asymptote at

x=1

, so no finite value exists. b) The integral converges and equals

1

. c) The integral diverges because the integrand is unbounded at

x=0

. d) The integral converges and equals

\dfrac{3}{2}