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Why no simplification ?

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
carlenC at

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