275. $\int_{-1}^{\sqrt{3} / 2} \frac{d x}{\sqrt{1-x^{2}}}$  
276. $\int_{0}^{0.5} \frac{d x}{\sqrt{1-4 x^{2}}}$  
277. $\int_{0}^{\sqrt{3}} \frac{d x}{1+x^{2}}$.
Solution. $\quad \int_{0}^{\sqrt{3}} \frac{d x}{1+x^{2}}=\operatorname{arctg} x \int_{0}^{\sqrt{3}}=\operatorname{arctg} \sqrt{3}-\operatorname{arctg} 0=\pi / 3-0=$ $=\pi / 3$.