${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{t\sqrt[\phantom{2}]{t}}dt=$

$(-\frac{3}{2}{t}^{-\frac{5}{2}}+C)$

$-\frac{2}{5}{t}^{-\frac{5}{2}}+C$

$2t^{\frac{1}{2}}lnt+C$