Chapter 4 - Integration - 4.5 Exercises - Page 301: 21

$-(1-x^{2})^{\frac{1}{2}}+C$

$let$ $1-x^{2}=u$ $du=-2x$ $dx$ $\int$$u^{-\frac{1}{2}}$ $du$ $=-\frac{1}{2}\int$$(1-x^{2})^{-\frac{1}{2}}$ $(12x^2)$ $dx$ $=-\frac{1}{2}(2(1-x^{2})^{\frac{1}{2}})+C$ $=-(1-x^{2})^{\frac{1}{2}}+C$