Could someone please explain how
∫∞0e−xxdx diverges?
This is because the Laplace transform of 1t 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.
Thanks in advance.
Answer
Regarding the second part of the question, to add to carmichael561's answer,
To use the limit comparison test with e−x, we need
e−xx≤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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