Evaluate $\int \left(\sqrt{x} + \frac{1}{\sqrt{x}}\right)\,dx$.

Explanation

1. 01

   Integrate term by term with the standard forms: $\int x^n\,dx = \frac{x^{n+1}}{n+1}$, $\int \frac{1}{x}\,dx = \log|x|$, $\int e^x\,dx = e^x$.

2. 02

   $\int \left(\sqrt{x} + \frac{1}{\sqrt{x}}\right)\,dx = \frac{2 x^{\frac{3}{2}}}{3} + 2 \sqrt{x} + C$.

3. 03

   Check: differentiating the answer gives back the integrand.