Answer
\[\begin{gathered}
\frac{{2\sqrt {4x + 1} }}{4} + C \hfill \\
\hfill \\
\end{gathered} \]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\frac{x}{{\sqrt {4x + 1} }}dx} \hfill \\
\hfill \\
use\,\,the\,\,\,\,formula \hfill \\
\hfill \\
\int {\frac{{dx}}{{\sqrt {ax + b} }}} dx = \frac{{2\sqrt {ax + b} }}{a} + C \hfill \\
\hfill \\
with\,\,a = 4\,\,and\,\,b = 1 \hfill \\
\hfill \\
then \hfill \\
\hfill \\
\int {\frac{{dx}}{{\sqrt {4x + 1} }}} = \frac{{2\sqrt {4x + 1} }}{4} + C \hfill \\
\end{gathered} \]
