Answer
$\frac{2}{5}x^{\frac{5}{2}} + x^{2} + x + C $
Work Step by Step
$\int (x^{\frac{3}{2}}+2x +1) dx $
$=\int x^{\frac{3}{2}} dx + \int2x dx + \int 1 dx $
$=\frac{x^{\frac{3}{2}+1}}{\frac{3}{2}+1} + \frac{2x^{1+1}}{1+1} + C'+ \int 1x^{0} dx $
$=\frac{x^{\frac{5}{2}}}{\frac{5}{2}} +\frac{2x^{2}}{2} + \frac{1x^{1}}{1} + C $
= $\frac{2x^{\frac{5}{2}}}{5}+ \frac{2}{2}x^{2} + x + C $
= $\frac{2}{5}x^{\frac{5}{2}} + x^{2} + x + C $
The result can be checked by differentiating, and it works.
