$$\int\limits_0^{ + \infty } {\frac{{dx}}{{{{\cosh }^{2n}}x}}} ,{\text{ }}\int\limits_0^{ + \infty } {\frac{{dx}}{{{{\cosh }^{2n + 1}}x}}} $$
$$\int\limits_0^{ + \infty } {\frac{{dx}}{{{{\cosh }^{2n}}x}}} = \frac{{\left( {2n - 2} \right)!!}}{{\left( {2n - 1} \right)!!}}$$
$$\int\limits_0^{ + \infty } {\frac{{dx}}{{{{\cosh }^{2n + 1}}x}}} = \frac{{\left( {2n - 1} \right)!!}}{{\left( {2n} \right)!!}} \cdot \frac{\pi }{2}$$
