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Question: How to get the Laplace inverse of this function? (maple leaves the integral unevaluated)

Question:How to get the Laplace inverse of this function? (maple leaves the integral unevaluated)

nidojan 130 Maple
integration inverse laplace
September 20 2021
1

kindly help me to find the inverse Laplace of this function. I tried but maple leaves the integral unevaluated.
 

> 

restart
> 

with(inttrans)
> 

expr := exp(a-sqrt(a^2+b*s))/s

exp(a-(a^2+b*s)^(1/2))/s

 (1)
> 

`assuming`([invlaplace(expr, s, t)], [b > 0])

(1/2)*(b/Pi)^(1/2)*(int(exp(-a^2*_U1/b+a-(1/4)*b/_U1)/_U1^(3/2), _U1 = 0 .. t))

 (2)
> 

NULL


 

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