Laplace transform of a weird function

[clustro]

So, the definition of Laplace transform is:

$$\int_{0}^{\infty} e^{-st} f(t) dt$$

what if:

$$f(t) = g(t)exp\Big[-\int_{0}^{t}g(t')dt'}\Big]$$

Or, in words: if the function being transformed is itself a function of an integral. This seems somewhat tough, but maybe I just not thinking correctly.

I don't think integration by parts is going to help us much here. :[

Any ideas?

 

[dextercioby]

I'm pretty sure that knowing who g(t) is would help you find an answer to your query.

 

[clustro]

Well yes, it would help, but I was wondering if a more general relation might be gained from the analysis.

For example, if you wanted to take the laplace transform of an integral, you could evaluate the integral, and then take its laplace transform.

Or you could just divide by s. -_-