Basic Examples 
(2)
 

The expression of this example has a known symbolic Laplace inverse:
In[96]:=
[◼]
NInverseLaplaceTransform
[Exp[1-Sqrt[s]]s^(-3/4),s,3.7]
Out[96]=
1.27511
We can compare the result with the answer from the symbolic evaluation:
In[97]:=
InverseLaplaceTransform[Exp[1-s^(1/2)]s^(-3/4),s,t]
Out[97]=
1-
1
8t

BesselK
1
4
,
1
8t

2
π
t
In[98]:=
%/.{t3.7}
Out[98]=
1.27511
———
This expression cannot be inverted symbolically, only numerically:
In[99]:=
expr2=((-1.+100.*s)*Sinh[0.5*Sqrt[s]])/(s*(Sqrt[s]*Cosh[Sqrt[s]]+s*Sinh[Sqrt[s]]));​​
[◼]
NInverseLaplaceTransform
[expr2,s,0.2727]
Out[100]=
30.658

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