\( f ( x ) = 5 + \frac { 1 } { 2 \sqrt { x } } \Rightarrow F ( x ) = \)

To find the indefinite integral \( F(x) \) of the function \( f(x) = 5 + \frac{1}{2\sqrt{x}} \), we integrate term by term. The integral of \( 5 \) is \( 5x \), and the integral of \( \frac{1}{2\sqrt{x}} \) is \( \sqrt{x} \). So, the full integral is: \[ F(x) = 5x + \sqrt{x} + C \] where \( C \) is the constant of integration. Enjoy finding the joys of calculus! When working with integrals involving roots, a common mistake is forgetting to properly account for the constant of integration \( C \). This is crucial because it reflects that there are infinitely many antiderivatives that differ only by a constant. So, always remember to include it!