For which values of k , where k is a Real number does the improper integral:
integral( (ln(x)^k) / (x) ) from 1 to infinity
converge? For which values of k does it diverge? Justify your answer.
In the exercise I meant that k is a real number, can take any value from -infinity to +infinity. The improper integral has lower limit 1 and upper limit +infinity.
Do you know if there is any specific range in which the improper integral diverges and any other range that the improper definite integral converges?
And who I can find this? By taking limits?
Thanks a lot!