Consider the indefinite integral $\displaystyle {\int_{{0}}^{{1}}}\frac{{x}^{{2}}}{{\left({x}^{{3}}-{3}\right)}^{{3}}}\ {\left.{d}{x}\right.}$:

This can be transformed into a basic integral by letting

$\displaystyle {u}=$ Preview Question 6 Part 1 of 5   and

$\displaystyle {d}{u}=$$\displaystyle {\left.{d}{x}\right.}$ Preview Question 6 Part 2 of 5  

Performing the substitution yields the integral

$\displaystyle {\int_{{a}}^{{b}}}$$\displaystyle {d}{u}$ Preview Question 6 Part 3 of 5  
where a = and b =