Find the following integral: $\int(2x^2 - 3\sin x + 5\sqrt{x}) dx$

We are given the integral $\int(2x^2 - 3\sin x + 5\sqrt{x}) dx$.
Using the linearity property of integration,we can write:
$\int(2x^2 - 3\sin x + 5\sqrt{x}) dx = 2\int x^2 dx - 3\int \sin x dx + 5\int x^{1/2} dx$.
Applying the power rule $\int x^n dx = \frac{x^{n+1}}{n+1} + C$ and the standard integral $\int \sin x dx = -\cos x + C$:
$= 2(\frac{x^3}{3}) - 3(-\cos x) + 5(\frac{x^{3/2}}{3/2}) + C$.
Simplifying the expression:
$= \frac{2}{3}x^3 + 3\cos x + 5(\frac{2}{3})x^{3/2} + C$.
Final result:
$= \frac{2}{3}x^3 + 3\cos x + \frac{10}{3}x^{3/2} + C$,where $C$ is an arbitrary constant.