integrate: is this question a bug?



Edwin Woollett wrote:
> Ray writes (this is good information for a neophyte to know!):
> 
> "It uses the internal variable yx and wants to solve the equation yx = exp(sqrt(x)) for x.  I guess it needs to know the sign of yx to solve this."
> 
> My naive comments:
> 
> 1. Minimal help to user: include this message inside of integrate() - user interaction when asking a question about an internal variable yx whose function is normally hidden from the user.

I suppose that's possible, but not very appealing.  Maxima shouldn't ask 
at all.
> 
> 2. More help to user: examine range of integration variable (x), determine if sign of integrand is constant over that integration range, and if so, determine the sign of yx from that information.

I think that's a hard problem in general, although it ought to be easy 
for this particular case since the exp(x) is always positive.  But 
maxima wasn't asking for the sign of x; it wanted the sign of yx.

> 
> 3. Even more help: split up the integral into a sum of integrals, for each of which one can determine the sign of yx.

I think that's basically equivalent to finding the roots of the 
integrand, which is quite hard.

I don't have a good solution for this.  But at least you now know what 
yx means. :-)

Ray