Consider the indefinite integral x6 x7+65 dx\displaystyle \int{x}^{{6}}\ \cdot{\sqrt[{{5}}]{{{x}^{{7}}+{6}}}}\ {\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: