How would I take the laplace transform of f(t)= te^tsin^2(t)?
You mean t et sin(2t)? What's causing you the problem? It is pretty straight-forward application of the definition case.
No the equation is f(t)= te^tsin^2(t)
Still, it's a standard case (I have a vague recall of this exact function class being important in telecommunication). Perfectly doable via integration by parts. Is this where you got stuck?
Kinda, Is there anyway to figure out the transform of sin^2(t) then use the theorem for the e^t and t?
I don't know of having seen that in a table anywhere, it doesn't look like an elementary form, so what you need to do is compute the transform directly using the Laplace transformation definition.
For integrating the sin2(t) in the transformation integral you need to use the half-angle formula: http://www.sosmath.com/trig/douangl/douangl.html
Thank you so much!
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