Consider the function \begin{align} f(t) = \frac{1}{e^{2t} + 1}. \end{align} Is it possible to evaluate the Laplace transform $L\lbrace f(t) \rbrace$ ?.
Thanks in advance.
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Are you familiar with $\int_0^\infty\frac{x^{z-1}dx}{1+x}=\pi\csc(z\pi)$ for $\Re z\in(0,,1)$? – J.G. Jan 27 '22 at 11:35
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It's the first time for me to see such a formula. @J.G. – Hussein Eid Jan 27 '22 at 11:39
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In that case, see e.g. here. – J.G. Jan 27 '22 at 11:44