Using $t=sec(),$ we get

${\displaystyle \underset{\sqrt[\phantom{2}]{2}}{\overset{2}{}}}\frac{1}{t^3\sqrt[\phantom{2}]{t^2-1}}dt={\displaystyle \underset{\frac{}{4}}{\overset{\frac{}{3}}{}}}\frac{se{c}^3()tan()}{se{c}^2()tan()d.}$

This can be further simplified to

${\displaystyle \underset{\frac{}{4}}{\overset{\frac{}{3}}{}}}\frac{?}{se{c}^2()}d$

or simply

${\displaystyle \underset{\frac{}{4}}{\overset{\frac{}{3}}{}}}co{s}^2()d$