Answer
\[ = \int_{}^{} {x + \frac{2}{3}{x^{\frac{3}{2}}} + C} \]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\frac{{1 - x}}{{1 - \sqrt x }}} \,dx \hfill \\
\hfill \\
{\text{rationalizing}} \hfill \\
\hfill \\
\int_{}^{} {\frac{{\,\left( {1 - \sqrt x } \right)\,\left( {1 + \sqrt x } \right)}}{{1 - \sqrt x }}} \,dx \hfill \\
\hfill \\
= \int_{}^{} {\,\left( {1 + \sqrt x } \right)} \,\,dx \hfill \\
\hfill \\
or \hfill \\
\hfill \\
\int {dx} + \int {{x^{1/2}}} dx \hfill \\
\hfill \\
integrate \hfill \\
\hfill \\
= \int_{}^{} {x + \frac{2}{3}{x^{\frac{3}{2}}} + C} \hfill \\
\end{gathered} \]
