Giá trị của \(\int\limits_0^{16} {\frac{{dx}}{{\sqrt {x + 9} - \sqrt x }}} \) là:

* Hướng dẫn giải

\(\begin{array}{l}I = \int\limits_0^{16} {\frac{{dx}}{{\sqrt {x + 9}  - \sqrt x }}} \\\,\,\,\,\, = \int\limits_0^{16} {\frac{{\left( {\sqrt {x + 9}  + \sqrt x } \right)dx}}{{x + 9 - x}}} \\\,\,\,\, = \int\limits_0^{16} {\frac{{\left( {\sqrt {x + 9}  + \sqrt x } \right)dx}}{9}} \\\,\,\,\, = \left. {\frac{1}{9}.\frac{2}{3}\left[ {\sqrt {{{\left( {x + 9} \right)}^3}}  + \sqrt {{x^3}} } \right]} \right|_0^{16}\\\,\,\,\, = \frac{2}{{27}}\left( {125 + 64 - 27 - 0} \right) = 12.\end{array}\)