Ответ:

Найти неопределённый интеграл .  

[tex]\bf \displaystyle 11)\ \ \int \frac{\sqrt[3]{\bf x}+2x-x^4}{x^5}\, dx=\int \frac{\sqrt[3]{\bf x}}{x^5}+2\int \dfrac{x}{x^5}-\int \frac{x^4}{x^5}\, dx=\\\\\\=\int x^{-14/3}\, dx+2\int x^{-4}\, dx-\int \frac{dx}{x}=\frac{5x^{-11/3}}{-9}+2\cdot \frac{x^{-3}}{-3}+ln|x|+C=\\\\\\=-\frac{5}{9\sqrt[3]{\bf x^{11}}}-\frac{2}{3x^3}+ln|x|+C[/tex]    

[tex]\bf \displaystyle 13)\ \ \int \Big(\frac{3}{8+5x^2}-\frac{1}{\sqrt{1-4x^2}}\Big)\, dx=\frac{3}{5}\int \frac{dx}{x^2+\dfrac{8}{5}}-\int \frac{dx}{\sqrt{1-(2x)^2}}=\\\\\\=\frac{3}{5}\cdot \frac{1}{\sqrt\dfrac{8}{5}}}}\cdot arctg\frac{x}{\sqrt{\dfrac{8}{5}}}}-\frac{1}{2}\cdot arcsin \frac{2x}{1}+C=\\\\\\=\frac{3}{2\sqrt{10}}\cdot arctg\frac{\sqrt5x}{2\sqrt2}-\frac{1}{2}\cdot arcsin(2x)+C[/tex]