[CAS] Integrals

[parisse]

DrD, I'm not sure you fully understand generallized integrals. For example int(ln(abs(x)),x,-1,1)=-2 despite the fact that ln(abs(x)) is not defined at x=0 inside the interval -1..1.
Every mathematician will agree that int(1/x^2,x,0,1) is a divergent integral, but a divergent integral to +infinity. The same is also true for int(1/x^2,x,-1,0). Therefore the sum is +infinity, it is not undefined.
int(1/x,x,0,1) is also +infinity, but int(1/x,x,-1,0) is -infinity therefore the sum is not well-defined, returning undef is perfectly acceptable. It might also be observed that by symmetry, the integrals compensate, and therefore returning 0 is also acceptable.
Conclusion: Wolfram alpha is not God, it's not because the Prime and Wolfram alpha disagree that the Prime is necessarily wrong.