We start from the relations (see the table of Laplace transforms)
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(1) |
The substitution
Thus we may write the formula
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(2) |
Moreover, we obtain
whence we have the other formula
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(3) |
One can utilise the formula (3) for evaluating the improper integral
We have
(see the table of Laplace transforms). Dividing this by
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and especially
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