Let u = 1 − x {\displaystyle u=1-x} . Then 1 ( 1 − x ) 3 / 2 = u − 3 / 2 {\displaystyle {\frac {1}{(1-x)^{3/2}}}=u^{-3/2}} , which is easy to take the integral of. Also be careful to note where the integrand blows up, and to resort to limits when necessary.
