[CAS] Integrals

[Arno K]

Well, not an easy task, it is based on the fact that the real numbers are defined without +∞ and -∞, so to solve integrals like that you have to calculate both the integrals on the left side and on the right side with not zero but an "a" as lower bound, for example \[\int_a^1 \! \frac{1}{x^{n}} \, \mathrm{d}x\]Then you have to perform
\[\lim_{a \rightarrow 0}-\frac{1}{n-1}+\frac{1}{(n-1)\cdot a^{n-1}}\]
this always leads to +∞, the left hand side makes, dependent on n, + or - infinity.
As both limits are no real numbers the integrals do not converge. Then there is the point with compactification of the real numbers, both plus and minus infinity are taken in, this often leads to conclusions like in my post above.
Arno