$\displaystyle\int \left( \sqrt[3]{x^2}+\dfrac{4}{x}\right)dx$
$=\displaystyle\int \left( x^{\frac{2}{3}}+\dfrac{4}{x}\right)dx$
$=\dfrac{3}{5}x^{\frac{5}{3}}+4\ln|x|+C$
$\displaystyle\int \left(x^2+\dfrac{3}{x}-2\sqrt{x}\right)dx$
$=\displaystyle\int \left( x^2+\dfrac{3}{x}-2.x^{\frac{1}{2}}\right)dx$
$=\dfrac{1}{3}x^3+3\ln|x|-\dfrac{4}{3}x^{\frac{3}{2}}+C$
