Could someone please explain how int_0^(oo) (e^(-x))/(x) dx diverges?



Answered question


Explain how 0 e x x d x diverges? This is because the Laplace transform of 1 t can be reduced to this integral which has to diverge. But the limit comparison test with e x shows that the integral converges.
Please help

Answer & Explanation

Brendan Bradley

Brendan Bradley

Beginner2022-09-07Added 11 answers

The issue is at zero:
0 1 e x x d x 1 e 0 1 d x x =
Therefore 0 e x x d x = 0 1 e x x d x + 1 e x x d x diverges
Drew Williamson

Drew Williamson

Beginner2022-09-08Added 2 answers

Regarding the second part of the question, to add to first's answer,
To use the limit comparison test with e x , we need
e x x e x
throughout the interval over which integral takes place.
However, this is true only for x>1, and hence the test cannot be used.

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