Should maxima be able to do this integral? (A.K.A. what am I missing?)



I'll readily concede I could be making a mistake here, but just in case
I'm not...  When I try the following integral:

(C1) integrate(1/(y*(y+1)),y);

(D1) 			      LOG(y) - LOG(y + 1)

which is fine and equals LOG(y/(y+1)).  But when I do a definite
integral from zero to inf, this happens:

(C9) integrate(1/(y*(y+1)),y,0,inf);

Integral is divergent
 -- an error.  Quitting.  To debug this try DEBUGMODE(TRUE);)

which initially looks like it makes sense, since log(y/(y+1)) doesn't
immediately look like it can be evaulated at the infinity limit,
although it can be evaluated at y=0.  But if we do a manipulation of
the results from the indefinite integral using Laws of Logarithms, we
get the form:

LOG(y) - LOG(y + 1)=-(LOG(y+1) - LOG(y))=-LOG(1+y/y)=-LOG(1+1/y)

which can be evaluated at inf but not at zero.  If we use the latter
form at inf and the first form at zero, which should be legal since the
two forms are equal? evaluating at the limits and subtracting gives us
for the integral:

-LOG(1)-LOG(0)=-1

I suppose I messed up and/or did something illegal somewhere, but can
someone enlighten me why this is wrong?  Sorry if this is an obvious
mistake on my part.

CY

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