0
$\begingroup$

Is the result of the of Laplace transform of $\int_1^\infty\frac{\cos t}{t}dt$ equal to $\frac{\int_1^\infty\frac{\cos t}{t}dt}{s}$?

  • 4
    Your integral is a constant, so...2012-07-17
  • 0
    ok, thanks. I just hope I don't have to solve the integral2012-07-17
  • 0
    It 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
  • 0
    You don't have to, unless you know the cosine integral.2012-07-17
  • 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 1

1

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 $F(s)={a\over s}$.