Please work out the following intergral
...what integral?
do you mean the one you put in the tag? why did you put it there?
anyway, make a substitution $\displaystyle t = \sqrt {x}$ (one way to make this work is to note that $\displaystyle x = \frac {(\sqrt{x})^3}{\sqrt{x}}$. another is to note that you can write $\displaystyle x = (\sqrt{x})^2 = t^2$, and solve for dx in terms of dt). the resulting integral you will be able to do by parts.
can you finish?