Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - Review Exercises - Page 579: 7

$=100\arcsin(\frac{x}{10})+C$

$\int\frac{100}{\sqrt {100-x^{2}}}dx$ Use $\int\frac{1}{\sqrt{(a)^{2}-(u)^{2}}}du=\arcsin(\frac{u}{a})+C$ $\int \frac{100}{\sqrt {100-x^{2}}}dx = \int\frac{100}{\sqrt{(10)^{2}-(x)^{2}}}dx$. $=100\arcsin(\frac{x}{10})+C$