An inequality for the product of two integrals relating to the incomplete gamma function (Q1973473)

Authors offer as main result the inequality \(F(x,p):=\int_0^x \exp(t^p) dt \int_x^{\infty} \exp(-t^p) dt <1/4\) for \(x\) nonnegative and \(p\) greater than the unique solution of \(\sup_{x>0} F(x,p)=1/4\) \((p\geq 1).\) Moreover inequalities (bounds) for the two integrals in \(F(x,p)\) are offered.