Question

What is the Laplace transform of e^(3pi - sqrt(2)*t)?

Answer 1

Anyone? This is the equation: \[e ^{3\pi - \sqrt{2}*t}\]

Answer 2

\[f(t)=e^{3\pi-\sqrt{2}t}=e^{3\pi}e^{-\sqrt{2}t}\]\[\mathcal{L}\{f(t)\}=\int\limits_0^{+\infty}f(t)e^{-st}dt=e^{3\pi}\int\limits_0^{+\infty}e^{-\sqrt{2}t}e^{-st}dt=e^{3\pi}\int\limits_0^{+\infty}e^{-(\sqrt{2}+s)t}dt=\]\[=\frac{e^{3\pi}}{s+\sqrt{2}}\]