\[\begin{array}{l} \int\limits_0^{ + \infty } {{e^{ - x \cdot t}}{{\sin }^{2n}}xdx} = \frac{{\left( {2n} \right)!}}{{t\prod\limits_{k = 1}^n {\left( {{t^2} + {{\left( {2k} \right)}^2}} \right)} }}, \hfill \\ \int\limits_0^{ + \infty } {{e^{ - x \cdot t}}{{\sin }^{2n + 1}}xdx} = \frac{{\left( {2n + 1} \right)!}}{{\prod\limits_{k = 0}^n {\left( {{t^2} + {{\left( {2k + 1} \right)}^2}} \right)} }}, \hfill \\ t > 0. \hfill \\ \end{array} \]