\[\int\limits_0^{\frac{\pi }{2}} {{{\operatorname{tg} }^s}x} dx,{\text{ }}0 < s < 1.\]
\[\int\limits_0^{\frac{\pi }{2}} {{{\operatorname{tg} }^s}x} dx = \int\limits_0^{\frac{\pi }{2}} {{{\left( {\sin x} \right)}^s}{{\left( {\cos x} \right)}^{ - s}}} dx = \frac{1}{2}{\rm B}\left( {\frac{{s + 1}}{2},\frac{{1 - s}}{2}} \right)\]
\[\frac{1}{2}{\rm B}\left( {\frac{{s + 1}}{2},\frac{{1 - s}}{2}} \right)\]
