# How do you find the indefinite integral of int (x^4-6x^3+e^xsqrtx)/sqrtx dx?

$\frac{2}{9} {x}^{\frac{9}{2}} - \frac{12}{7} {x}^{\frac{7}{2}} + {e}^{x} + C$
$\int \frac{{x}^{4} - 6 {x}^{3} + {e}^{x} \sqrt{x}}{\sqrt{x}} \mathrm{dx} = \int \left({x}^{\frac{7}{2}} - 6 {x}^{\frac{5}{2}} + {e}^{x}\right) \mathrm{dx}$
$= \frac{1}{\frac{7}{2} + 1} {x}^{\frac{7}{2} + 1} - \frac{6}{\frac{5}{2} + 1} {x}^{\frac{5}{2} + 1} + {e}^{x} + C$