What is the Laplace transform of 1/(1+t)

Cory Russell 2022-10-27 Answered
What is the Laplace transform of 1 1 + t
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Answers (1)

benyaep17
Answered 2022-10-28 Author has 11 answers
It is an exponential integral.
L { 1 1 + t } = 0 e s t t + 1 d t
We can get the Laplace transform by letting u = 1 + t. Then d u = d t and we have
0 e s t t + 1 d t = 1 e s u + s u d u = e s 1 e s u u d u
where 1 e s u u d u = Ei ( s ). Thus
L { 1 1 + t } = e s Ei ( s ) .
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