Is it possible to get the following integral involving vectors done in Maple 2018, but handle the singularity when p1=p3?

Note that the output of p3 and p1 are slightly different, probably because the earlier version of the worksheet was in Maple 2017?

(Note: Earlier version - was due to help received from Dr. Edgardo Cheb-Terrab, using Maple 2017).

with(Physics[Vectors]);
r_ := _i*x+_j*y+_k*z;
r_ := _i x + _j y + _k z
p__1_ := _i*`p__1x `+_j*`p__1y `+_k*`p__1z `;
p__1_ := _i p__1x + _j p__1y + _k p__1z
p__3_ := _i*`p__3x `+_j*`p__3y `+_k*`p__3z `;
p__3_ := _i p__3x + _j p__3y + _k p__3z
Expression to integrate wrt p3
'exp(i*(p__1_ . r_))/((p__3_ - p__1_)^2)'
exp(I Physics:-Vectors:-.(p__1_, r_))
-------------------------------------
2
Physics:-Vectors:-+(p__3_, -p__1_)
Delaying the evaluation above, if evaluation is allowed, the integrand is
exp(I*(p__1_ . r_))/(p__3_-p__1_)^2;
(exp(I (p__1x x + p__1y y + p__1z z)))/((_i (-p__1x + p__3x )
+ _j (-p__1y + p__3y ) + _k (-p__1z + p__3z ))^2)
T i is the imaginary unit
interface(imaginaryunit = I);
I
Because (4), has the value of i before being the imaginary unit, input the integrand again
'exp(i*(p__1_ . r_))/((p__3_ - p__1_)^2)'
exp(I Physics:-Vectors:-.(p__1_, r_))
-------------------------------------
2
Physics:-Vectors:-+(p__3_, -p__1_)
Now on the integration
Int(exp(I*(p__1_ . r_))/(p__3_-p__1_)^2, [`p__3x ` = -infinity .. infinity, `p__3y ` = -infinity .. infinity, `p__3y ` = -infinity .. infinity]);
/infinity /infinity /infinity
| | |
| | | (exp(I (p__1x x + p__1y y
| | |
/-infinity /-infinity / -infinity
+ p__1z z)))/((_i (-p__1x + p__3x ) + _j (-p__1y + p__3y )
+ _k (-p__1z + p__3z ))^2) dp__3x dp__3y dp__3y
value(Int(exp(I*(`p__1x `*x+`p__1y `*y+`p__1z `*z))/(_i*(-`p__1x `+`p__3x `)+_j*(-`p__1y `+`p__3y `)+_k*(-`p__1z `+`p__3z `))^2, [`p__3x ` = -infinity .. infinity, `p__3y ` = -infinity .. infinity, `p__3y ` = -infinity .. infinity]));
/ /[
exp(I (p__1x x + p__1y y + p__1z z)) |PIECEWISE|[infinity,
\ \[
Im(_i p__1x + _j p__1y + _k p__1z - _k p__3z ) ]
------------------------------------------------- = 0],
_i ]
\\
[0, otherwise]|| infinity
//
In the above, there is the product of three Dirac delta functions, that can be represented as a single 3D Dirac delta
combine(exp(I*(`p__1x `*x+`p__1y `*y+`p__1z `*z))*piecewise(Im(_i*`p__1x `+_j*`p__1y `+_k*`p__1z `-_k*`p__3z `)/_i = 0, infinity, 0)*infinity);
/ /[
exp(I (p__1x x + p__1y y + p__1z z)) |PIECEWISE|[infinity,
\ \[
Im(_i p__1x + _j p__1y + _k p__1z - _k p__3z ) ]
------------------------------------------------- = 0],
_i ]
\\
[0, otherwise]|| infinity
//