Ответ:

Найти неопределённый интеграл .

[tex]\bf \displaystyle \int \Big(x^2-2x\sqrt{x}+3\sqrt[3]{\bf x}+\frac{5}{x}\Big)\, dx=\\\\\\=\int \,x^2\, dx-2\int x^{3/2}\, dx+3\int x^{1/3}\, dx+\int \frac{5}{x}\Big)\, dx=\\\\\\=\frac{x^3}{3}-2\cdot \frac{2x^{5/2}}{5}+3\cdot \frac{3x^{4/3}}{4}+5\cdot ln|x|+C=\\\\\\=\frac{x^3}{3}-\frac{4\sqrt{x^{5}}}{5}+\frac{9\sqrt[3]{\bf x^{4}}}{4}+5\cdot ln|x|+C=[/tex]  

[tex]\bf \displaystyle 10)\ \ \int \Big(\sqrt{x}-\frac{3}{\sqrt[5]{x}}\Big)^2\, dx=\int \Big(x-2\sqrt{x}\cdot \frac{3}{\sqrt[5]{\bf x}}+\frac{9}{\sqrt[5]{\bf x^2}}\Big)\, dx=\\\\\\=\int \Big(x-6\cdot x^{3/10}+9\cdot x^{{-2/5}}\Big)\, dx=\frac{x^2}{2}-6\cdot \frac{10\, x^{13/10}}{13}+9\cdot \frac{5x^{3/5}}{3}+C=\\\\\\=\frac{x^2}{2}-\frac{6\sqrt[10]{\bf x^{13}}}{13}+\frac{45\sqrt[5]{\bf x^5}}{3}+C[/tex]