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Laplace transform of cos t and polynomials

Laplace transform of cosine and polynomials! Created by Sal Khan.

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• AT shouldn't it be PLUS zero not MINUS?
• Either way, adding or subtracting zero wouldn't change the outcome would it...because neither would change anything, right?
• What if n is not a positive integer? Then we can't have a factorial, any formulas for this case?
• As far as integration by parts go, if n<0 the laplace transform of t^n will either give rise to a division by zero or go on forever. It will probably diverge for cases where n<0. Searching though tables, they only show the laplace transform for when n=>0.
• Can U PLZ upload a video for existence of Laplace Transforms...
• Can anyone recommend a good source of practice questions (a website etc) on Laplace transforms?
• At 5.43, is it meant to be minus zero, or plus zero as in the formula on the right hand side?
• You're correct. In this case, it just happens the result is same
• What is the Laplace transform of h(t)= 5 cos(2t – 1)u(t)
• Please post homework problems on another forum. You're not in the right place for such.
• Is there a case where cos or sin is squared? like (cos2t)^2 and (sin2t)^2 and if yes what is there laplace transform? Thanks.
• Yes, you can just replace cos²(θ) with ½ + ½ cos(2θ) and sin²(θ) with ½ - ½ cos(2θ).
• what is laplace transform of a^n????
• a^n is a constant so the transform would be:
L{a^n} = a^nL{1} = a^n(1/s) = a^n/s