1)\( \int x^{\frac{1}{2}}\, dx \)
\(\frac{2}{3} x^{\frac{3}{2}} + c\)
2)\( \int 3x^{-\frac{2}{7}}\, dx\)
\( \frac{21}{5}x^{\frac{5}{7}} + c\)
3)\( \int (4x^{\frac{3}{4}}+ 2x^{-\frac {2}{3}})\, dx\)
\( \frac{16}{7}x^ {\frac{7}{4}}+ 6 x^{\frac{1}{3}} + c\)
4)\( \int (3x^{-\frac{2}{5}}- 5x^{-\frac {7}{4}})\, dx\)
\( 5x^ {\frac{3}{5}}+ \frac{20}{3} x^{-\frac{3}{4}} + c\)
5)\( \int (\frac{3}{x^2} + \frac{4x}{x^3}) \, dx\)
\(-3x^{-1} - 4x^{-1} + c\)
6)\( \int \frac {5x+3}{x^3} \, dx\)
\(- 5x^{-1} - \frac{3}{2}x^{-2} + c\)
7)\( \int \frac{\sqrt{x} + 5x^3}{x}\, dx\)
\( \frac{2}{3}x^{\frac{3}{2}}+ \frac{5}{3} x^3 + c\)
8)\(\int \frac {(3x+1)^2}{\sqrt[3]{x} } \, dx\)
\( \frac{27}{10}x^{\frac{10}{3}} + \frac{18}{7}x^{\frac{7}{3}} + \frac{3}{2}x^{\frac{2}{3}} + c\)