[m] ∫_{0} ^{0,5}\frac{arctgx}{x}dx=∫_{0} ^{0,5}\frac{x-\frac{x^3}{3}+\frac{x^5}{5}-...}{x}dx=∫_{0} ^{0,5}(\frac{x}{x}-\frac{\frac{x^3}{3}}{x}+\frac{\frac{x^5}{5}}{x}+...)dx=∫_{0} ^{0,5}(1-\frac{x^2}{3}+\frac{x^4}{5}+...)dx=(x-\frac{x^3}{9}+\frac{x^4}{25}+...)|_{0} ^{0,5}=[/m]