Question 4

For each of the following integrals, give an appropriate substitution that will enable the integral to be carried out.
Also give the integral that results from the substitution.
You do not need to evaluate the subsequent integral.

• $${\int \frac{1}{x - \sqrt[3]{x}} \hspace{3pt}dx}$$.
  
  
  
  
  
  
  
  
  
  
  
  
  
• $${\int_{e}^{e^4} \frac{(\ln(t))^5}{t} \hspace{3pt}dt}$$.
  
  
  
  
  
  
  
  
  
  
  
  
  
• $${\int_1^4 \frac{x^3}{(1 + x^2)^{3}} \hspace{3pt}dx}$$.