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

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)

Try:

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