7.81 bug in integration 1 in Maple V.4 and Maple V.5 (13.5.98)

7.81.1 Marko Horbatsch

Can anyone explain the following integration error in Maple (Mma 3.0 has no problem with these integrals)

It is a class of integrals over the entire real axis over a bell-shaped function, where the location of the hump is displaced (which should not affect the calculation of the area under the curve). When the hump is centered at $x=0$, the calculation is fine, but when the hump is displaced along the real axis by an undetermined (real) amount, the integration answer is wrong (negative infinity).

Users beware, Developers fix this up please (happens in V4 and V5!)

restart; assume(v,real); assume(w>0); 
 
int(1/(x^2+w^2)^2,x=-infinity..infinity); 
1/2*Pi/w^3 
 
int(1/((x-v)^2+w^2)^2,x=-infinity..infinity); 
-infinity 
 
int(1/((x-v)^2+2)^2,x=-infinity..infinity); 
-infinity 
 
int(1/((x+3)^2+w^2)^2,x=-infinity..infinity); 
-infinity 
 
int(1/((x+3)^2+4)^2,x=-infinity..infinity); 
1/16*Pi
 

It is corrected with Maple 6. (U. Klein)

7.81.2 Willard, Daniel, Dr., DUSA-OR (28.5.98)

Try:

assume(w>0); limit(int(1/((x-v)^2+w^2)^2, x=-R..R), R=infinity);