\(x^{2}\sqrt{x} \equiv x^{2}. x^{\frac{1}{2}} = x^{\frac{5}{2}}\)
\(\implies \frac{\mathrm d y}{\mathrm d x} = x^{\frac{5}{2}}\)
\(y = \int x^{\frac{5}{2}} \mathrm d x\)
= \(\frac{x^{\frac{5}{2} + 1}}{\frac{5}{2} + 1} + c\)
= \(\frac{2x^{\frac{7}{2}}}{7} + c\)