Is the result of the of Laplace transform of $\int_1^\infty\frac{\cos t}{t}dt$ equal to $\frac{\int_1^\infty\frac{\cos t}{t}dt}{s}$?
Laplace transform of $ \int_1^\infty\frac{\cos t}{t}dt$
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ordinary-differential-equations
laplace-transform
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4Your integral is a constant, so... – 2012-07-17
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0ok, thanks. I just hope I don't have to solve the integral – 2012-07-17
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0It does converge (it resembles a convergent alternating series) and is a particular value of the so called [cosine integral](http://mathworld.wolfram.com/CosineIntegral.html). I'm not sure if its value can be explicitly computed. – 2012-07-17
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0You don't have to, unless you know the cosine integral. – 2012-07-17
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0@David: "I'm not sure if its value can be explicitly computed." - there's no simpler/elementary closed form, but you can *numerically* evaluate it, of course. – 2012-07-17
1 Answers
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Yes, it is. Note that you have a definite integral which, indeed, converges (it is a variant of the Cosine Integral). As such, you are finding the Laplace transform of a constant function. Of course, for a function $f$ with rule $f(t)=a$, its Laplace transform is $F(s)={a\over s}$.