2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160741Let $Δ(x)$ be the error term of the Dirichlet divisor problem. An asymptotic formula with the error term $O(T^{53/28+ε})$ is established for the integral $\int_1^TΔ^4(x)dx.$ Similar results are also established for some other well-known error terms in the analytic number theory .21 PagesNumber Theory11N37, 11M06text