It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a function is related to the antiderivative of this function by a simple convolution. This allows ...
The definite integral $M(a)\coloneq \frac{4}{\pi}\int_{0}^{\pi /2}\frac{x^{2}dx}{x^{2}+\text{ln}^{2}(2e^{-a}\text{cos}x)}$ is related to the Laplace transform of the ...
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