Why no simplification ?

*Subject*: [mg2536] Why no simplification ?*From*: crobc at epix.net (Christopher R. Carlen)*Date*: Fri, 17 Nov 1995 05:19:29 GMT*Approved*: usenet@wri.com*Distribution*: local*Newsgroups*: wri.mathgroup*Organization*: epix.net*Sender*: daemon at wri.com ( )

I evaluated the integral Integrate[ Sqrt[4t^2 + 4 + t^-2], {t, 1, E} ] by hand, which of course works out to E^2. By adding the terms over the common denominator t^2, a perfect square trinomial results in the numerator. Taking the square root yields just Integrate[ (2t^2 + 1)/t, {t, 1, E} ] which is valid for t > 0 . Now I can understand that Sqrt[ x^2 ] really can't be simplified to x, but is really |x| . But in the case of a perfect square trinomial like the above, which is always positive, why doesn't Mathematica recognize this ? Because it fails to recognize this simplification, the output is a big mess, containing another integral. But anyone can see that this is really quite a simple integral. Anyone have any ideas how to get this integral to come out in a more simple manner ? _____________________ Christopher R. Carlen crobc at epix.net carlenC at cs.moravian.edu