What does it mean when an integrand is singular at x = 0?

Question

the integrand $f(x) = x^{−1}sin(x^{−1}log(x))$ has infinitely many oscillations in the interval [0, 1] and is also singular at x = 0.

What does it mean "singular at x = 0"?

Answer 1

In this context, "singular at $x=0$" refers to the fact that the integrand has a singularity at $x=0$. In particular, our function fails to be defined at $x=0$.