Judging from this http://www.mathworks.nl/help/symbolic/int.html the code you would need is:
int(1/(exp(1000*(t^2 + 100)^(1/2))*(t^2 + 100)^(1/2)), t , 1,Inf)
Or perhaps you can use
t == 1..inf
And wrap it with vpa
like in the example, rather than with double
.