|   | 1 |  initial version  | 
Somehow the simply_full() works. It probably forces the integration to happen.
sage: integrate(1/sqrt(1+x^2/n),x,1,2).simplify_full()
-(arcsinh(1/sqrt(n)) - arcsinh(2/sqrt(n)))*sqrt(n)
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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.