Q$8(10$ points$)$

If we have an improper integral that equals a finite number, we say the integral converges. Otherwise, the integral diverges.

Show that ${\displaystyle \underset{4}{\overset{}{}}}\frac{1}{x}dx$ diverges.

Show that ${\displaystyle \underset{4}{\overset{}{}}}\frac{1}{x+1}dx$ diverges.

Show that ${\displaystyle \underset{4}{\overset{}{}}}\frac{1}{x}-\frac{1}{x+1}dx$ converges.