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UnkleRhaukus
 4 years ago
\[\mathcal{L}\{t^2sinh(3t)\}=\]
UnkleRhaukus
 4 years ago
\[\mathcal{L}\{t^2sinh(3t)\}=\]

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nikvist
 4 years ago
Best ResponseYou've already chosen the best response.1\[\sinh{3t}=\frac{e^{3t}e^{3t}}{2}\]\[\mathcal{L}\{t^2\sinh{3t}\}=\int\limits_0^{+\infty}t^2\sinh{3t}\cdot e^{st}dt=\]\[=\int\limits_0^{+\infty}t^2\frac{e^{3t}e^{3t}}{2}\cdot e^{st}dt=\]\[=\frac{1}{2}\left(\int\limits_0^{+\infty}t^2e^{(s3)t}dt\int\limits_0^{+\infty}t^2e^{(s+3)t}dt\right)\]\[\mathcal{L}\{t^2\}=\int\limits_0^{+\infty}t^2e^{st}dt=\frac{2}{s}\int\limits_0^{+\infty}te^{st}dt=\frac{2}{s^2}\int\limits_0^{+\infty}e^{st}dt=\frac{2}{s^3}\]\[\mathcal{L}\{t^2\sinh{3t}\}=\frac{1}{2}\left(\frac{2}{(s3)^3}\frac{2}{(s+3)^3}\right)=\]\[=\frac{1}{(s3)^3}\frac{1}{(s+3)^3}=\frac{18(s^2+3)}{(s^29)^3}\]
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