Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises - Page 52: 82

$\frac{1}{(1-x^{2})^{3/2}}$

We factor out $(1-x^2)^{-1/2}$, similar to Exercise 81: $\displaystyle \frac{(1-x^{2})^{1/2}+x^{2}(1-x^{2})^{-1/2}}{1-x^{2}}=\frac{(1-x^{2})^{-1/2}(1-x^{2}+x^{2})}{1-x^{2}}=\frac{1}{(1-x^{2})^{3/2}}$