Answer
$$ 2 \left( \frac{2^{ \sqrt{x} }}{\ln 2}\right) +c$$
Work Step by Step
Given $$\int \frac{2^{\sqrt{x}}}{\sqrt{x}} d x$$
Let $u=\sqrt{x} \ \ \Rightarrow \ \ du =\dfrac{dx}{2\sqrt{x}} $, then
\begin{align*}
\int \frac{2^{\sqrt{x}}}{\sqrt{x}} d x&=2\int 2^{u } d u\\
&= 2 \left( \frac{2^{u }}{\ln 2}\right) +c\\
&= 2 \left( \frac{2^{ \sqrt{x} }}{\ln 2}\right) +c
\end{align*}
