Integral Question

[uberathlete]

Hi everyone. I just wanted to ask if this integral can actually be found even without the function being explicitly shown:

int [ [e^(at)] Q(t) ] dt where 'a' is a constant

Is there a general form to this integral or does Q(t) actually have to be explicitly written out in order to get the integral?

The same question I guess pertains to something like this:

int Q(t) dt = ?

I mean, the integral should be [something] such that d[something]/dt should equal Q(t). But what is that [something] ?

I've been trying to figure this out forever but with no luck . Any help on this would be much appreciated. Thanks!

 

[royhaas]

In general, you need an explicit indefinite integral (anti-derivative) for Q. In practice, this means Q is a polynomial, exponential, or sine/cosine (complex exponential).