Find the integral`int(x^3+3x+4)/(sqrt(x))dx`

Explanation

To solve the integral \(\int \frac{x^3 + 3x + 4}{\sqrt{x}} \, dx\), we will first simplify the integrand by dividing each term in the numerator by \(\sqrt{x}\).

### Step 1: Simplify the integrand
We can rewrite the integrand as follows:
\[ \frac{x^3}{\sqrt{x}} + \frac{3x}{\sqrt{x}} + \frac{4}{\sqrt{x}} = x^{3 - \frac{1}{2}} + 3x^{1 - \frac{1}{2}} + 4x^{0 - \frac{1}{2}} = x^{\frac{5}{2}} + 3x^{\frac{1}{2}} + 4x^{-\frac{1}{2}} \]

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