Standard Laplace transform pairs (Q1673)

\\mathcal{L}\\{1\\}=\\frac{1}{s},\\quad \\mathcal{L}\\{t^{n}\\}=\\frac{n!}{s^{n+1}},\\quad \\mathcal{L}\\{e^{at}\\}=\\frac{1}{s-a},\\quad \\mathcal{L}\\{\\cos\\omega t\\}=\\frac{s}{s^{2}+\\omega^{2}},\\quad \\mathcal{L}\\{\\sin\\omega t\\}=\\frac{\\omega}{s^{2}+\\omega^{2}}