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Inverse Laplace Transform of $$$\frac{\ln\left(s - 1\right)}{s^{2}}$$$
Related calculator: Laplace Transform Calculator
Your Input
Find $$$\mathcal{L}^{-1}_{s}\left(\frac{\ln\left(s - 1\right)}{s^{2}}\right)$$$.
Answer
The Inverse Laplace transform of $$$\frac{\ln\left(s - 1\right)}{s^{2}}$$$A is $$$i \pi t + \frac{t^{3} \left(- \frac{\gamma \left(\frac{2 - 2 t}{t^{2}} - \frac{2}{t^{2}}\right)}{2} - \frac{\left(\frac{2 - 2 t}{t^{2}} + \frac{2 t - 4}{t^{2}}\right) e^{t}}{2} - \frac{\left(\frac{2 t - 2}{t^{2}} + \frac{2}{t^{2}}\right) \left(- \ln\left(t e^{2 i \pi}\right) + \operatorname{Ei}{\left(t \right)} + 2 i \pi\right)}{2} - \frac{2 t - 2}{2 t^{2}} - \frac{2}{t^{2}}\right) - t^{2} \ln\left(t e^{i \pi}\right) - \gamma t^{2} + t^{2}}{t}.$$$A