Evaluate the integral using substitution:
dx(3x+3)3\displaystyle \int{\frac{{{\left.{d}{x}\right.}}}{{{\left({3}{x}+{3}\right)}^{{3}}}}}


a) Let u = 
 

b) Thus, du=\displaystyle {d}{u}=  

c) So, the integral written in terms of u\displaystyle {u} is \displaystyle \int  

d) Now, finish evaluating the integral and write your answer in terms of x\displaystyle {x}: dx(3x+3)3\displaystyle \int{\frac{{{\left.{d}{x}\right.}}}{{{\left({3}{x}+{3}\right)}^{{3}}}}} =