Answer
$$F(x) = x-2\cos x+6x^{1/2} +C$$
Work Step by Step
Given $$f(x) = 1+2\sin x+3/\sqrt{x}= 1+2\sin x+3x^{-1/2}$$
Then by using table 2 if $f(x)= x^n\ \to\ \ F(x) = \frac{x^{n+1}}{n+1} +C$ and if
$f(x)=\sin x\ \to\ \ F(x) =-\cos x +C$
Hence
\begin{align*}
F(x)&= x-2\cos x+\frac{3}{1/2}x^{1/2}+C \\
&= x-2\cos x+6x^{1/2} +C
\end{align*}
To check
\begin{align*}
F'(x) &= 1+2\sin x+3x^{-1/2} \\
&= 1+2\sin x+3/\sqrt{x}\\
&=f(x)
\end{align*}
