Simplifying a Double Integral: No Known Anti-Derivative

[CharmedQuark]

Homework Statement

The equation is $$\int^{t}_{0}$$e$$^{-t'\gamma}$$$$\int^{t}_{0}$$e$$^{t''\gamma}$$f(t'')dt''dt'. f(t) is a random function with no known anti-derivative. I need to simplify this into a single integral of one variable.

Homework Equations

above.

The Attempt at a Solution

I moved the first exponential function inside the second integral but none of the regular properties of double integrals seem to work here. Does anyone have any ideas?

 

[Avodyne]

As written you have simply the product of two integrals,

$$\left[\int^{t}_{0}e^{t'\gamma}dt' \right] \left[ \int^{t}_{0}e^{t''\gamma}f(t'')dt''\right]$$

and the first one is simple.

 

[CharmedQuark]

No, It's not a typo. I had no idea that that could be done. Thank you this makes this a lot easier.