Improper integral

[Maro]

Hello Bernard,

it seems that CAS indeed has a problem with NthROOT command. You can simply check it by using the „int(...)“ command for determining the antiderivative of the function f(x)=1/(5thROOT(x-1)). If you evaluate the result at x=33 you will get 40, which is wrong (it should be 20)

The antiderivative given by „int(1/5thROOT(x-1)) is in principle correct, but in the non simplified result there is a (-5)thROOT expression used, which is obviously evaluated wrong by the CAS.

When doing the same with fractional power 1/(x-1)^1/5 the antiderivative and the evaluation at x=33 is fine. It gives 20.

Compare CAS and Home with calculating (-5)thROOT(32), which results in „1“ (CAS) or in „0.5“ (HOME, which is correct). (-N)thROOT(x) should always be the same as x^(-1/N)

Regards
Maro