SSIA...
i checked through all theexamples and have no idea how to even begin..i would really appreciate it if someone pointed me in the right direction..thanks
Because if this was $\displaystyle \int e^{\sqrt{x}}$ I might see where you are coming from but we are integrating $\displaystyle \int e^{\sqrt{x}}\color{red}dx$ so we have to find a replacement for $\displaystyle e^{\sqrt{x}}$ which we do by replacing $\displaystyle x$ with $\displaystyle z^2$ and we have to replace $\displaystyle dx$ by $\displaystyle 2z\:dz$