Consider the indefinite integral x4x52 dx\displaystyle \int\frac{{x}^{{4}}}{{{x}^{{5}}-{2}}}\ {\left.{d}{x}\right.}:

a) This can be transformed into a basic integral by letting

u=\displaystyle {u}=   and

du=\displaystyle {d}{u}=  

b) Performing the substitution yields the integral

\displaystyle \int  

c) Once we integrate and substitute, the final answer in terms of x is: