- #1

arestes

- 80

- 3

- TL;DR Summary
- direct definition of the LT of cos(t)/t diverges. However wolframalpha computes it and gives a result with log and Euler Mascheroni constant

So, I know the direct definition of the Laplace Transform:

$$ \mathcal{L}\{f(t) \} = \int_0^\infty e^{-st}f(t)dt$$

So when I plug in:

$$\frac{\cos(t)}{t}$$

I get a divergent integral.

however:https://www.wolframalpha.com/input/?i=+Laplace+transform+cos(t)/(t)

is supposed to be the L.T. What is wolframalpha computing? Am I mistaken in something above?

$$ \mathcal{L}\{f(t) \} = \int_0^\infty e^{-st}f(t)dt$$

So when I plug in:

$$\frac{\cos(t)}{t}$$

I get a divergent integral.

however:https://www.wolframalpha.com/input/?i=+Laplace+transform+cos(t)/(t)

is supposed to be the L.T. What is wolframalpha computing? Am I mistaken in something above?