How to solve this Laplace transform? $f(t)=e^{2t}\cos^2 3t  3t^2 e^{3t}$
2,218
Remember that
$$\cos^2(3t) = \frac{1+\cos(6t)}{2}$$
and
$$\mathcal{L}(t^n f(t)) = (1)^n \frac{d^n}{ds^n} F(s).$$
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Admin
Updated on October 01, 2020Comments

Admin about 3 years
Find the laplace transform of
$$f(t)=e^{2t}\cos^2 3t  3t^2 e^{3t}$$
The answer is $$\frac{1}{2(s+2)}+ \frac{1}{2} \frac{s+2}{s^2 + 4s + 40}  \frac{6}{(s3)^3}.$$
This took me about an hour to solve, which seems ridiculously long. I probably did things inefficiently, how can this be solved?
My method: Separate using linearity and then integrate by parts, with partial fraction decomposition.

Admin about 9 yearsEdited to be objective.(in reference to the close vote)

JP McCarthy about 9 yearsYou must not have done the shift theorem yet... this will make things much easier for you.
