Chapter 7.1, Problem 52E

Show that the function $f\left(t\right)=1/t^2$ does not possess a Laplace transform. [Hint Write $L\left\{1/t^2\right\}$ as two improper integrals:

$L\left\{1/t^2\right\}={\displaystyle {\int }_0^1\frac{e^{-st}}{t^2}dt+{\displaystyle {\int }_1^{\infty }\frac{e^{-st}}{t^2}dt=I_1+I_2.}}$

Show that I₁ diverges.]