|   | 1 |  initial version  | 
I can confirm that this problem also occurs with the integral to 11/40.
That said,
sage: i
1/((1.31926121372032*x + 0.00329815303430079)/(1.31926121372032*x + 1.00329815303430) - x/(x + 1))
and usually Maxima does not particularly like integrating floating point things exactly, because it sort of doesn't make sense.
sage: numerical_integral(i,0,0.275)
(12.325862793647284, 4.191806193893343e-11)
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                Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.