Let us calculate the value of this intergral numerically using the adaptive quadrature with machine precision. The result is
Almost same result is obtained by evaluating analytically
We therefore conclude that it is likely that the statement that is true.
Note that this calculation does not provide a proof that this is true, only a demonstration that this is plausible assumption. Differnce in the last few digits are to be expected due to the complexity of this integral.
so we conclude that , so that this statement is also likely to be true.
We emphasize that using numerical methods to analyze analytic formulas of this kind can confidently proove that , but can only give indications that , with out prooving it.