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Question Number 203199 by MathedUp last updated on 12/Jan/24

$${\mathrm{Let}}^{\prime }s\mathrm{define}\mathrm{linear}\mathrm{Operator}\mathcal{L}\mathrm{as}\mathcal{L}={\int }_0^{\mathrm{\infty }}{e}^{-st}\cdot$$$$\mathcal{L}\left\{W\left(t\right)\right\}=???$$$$W\left(t\right)\mathrm{is}\mathrm{inverse}\mathrm{function}\mathrm{of}y\left(t\right)={te}^t,t\in [-\frac{1}{e},\mathrm{\infty })$$

Commented by shunmisaki007 last updated on 13/Jan/24

$$\mathrm{I}\mathrm{have}\mathrm{removed}\mathrm{my}\mathrm{answer}\mathrm{to}\mathrm{apologize}$$$$\mathrm{my}\mathrm{misunderstanding}.$$$$\mathrm{However},\mathrm{I}\mathrm{still}\mathrm{have}\mathrm{no}\mathrm{way}\mathrm{to}\mathrm{find}$$$$\underset{0}{\stackrel{\mathrm{\infty }}{\int }}{e}^{-st}W\left(t\right)dt.$$

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