[tex]\displaystyle\bf\\\int \frac{1}{x}dx=ln|x|.\\\int \frac{1}{x^n}dx=-\frac{1}{\bigg(n-1\bigg)x^{n-1}}.\\---------------------------------\\\int \frac{1+\sqrt{x}}{x}dx=\int \frac{1+x^{\frac{1}{2}}}{x}dx=\int\frac{1}{x}+\frac{x^{\frac{1}{2}}}{x}dx=\int \frac{1}{x}dx +\int\frac{x^{\frac{1}{2}}}{x}dx=\\ln|x|+\int \frac{1}{x^{\frac{1}{2}}}dx=ln|x|+2\sqrt{x}+\mathcal{C}.[/tex]
