#### 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);