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