Can't solve an integral?

Questions
1

Hello, I would be happy to learn why MATHEMATICA is unable to resolve analytically the following integral:

Integrate[Exp[-a/(t-tau)]/Sqrt[t-tau],{tau,0,t},Assumptions->{a>0}];

As far as I am aware, the integral exists and it is

2*Sqrt[t]*Exp[-a/t]-2*Sqrt[Pi*a]*Erfc[Sqrt[a/t]]

However MATHEMATICA concludes the integral does not converge. Is there any way to get the correct result?

Leslaw

2

Just add the assumption that t>0.

3

Agreed it is unfortunate that this claims divergence when it behave just fine under the assumption noted by Gianluca Gorni. The takeaway, nonetheless, is that helping Integrate with assumptions can be vital, both for correctness and speed (less time spent sorting out issues of convergence).