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In this paper, we derive a formula on the integral of products of thehigher-order Euler polynomials. By the same way, similar relations are obtainedfor $l$ higher-order Bernoulli polynomials and $r$ higher-order Eulerpolynomials. Moreover, we establish the connection between the results and thegeneralized Dedekind sums and Hardy--Berndt sums. Finally, the Laplacetransform of Euler polynomials is given.

On the integral of products of higher-order Bernoulli and Euler polynomials