Hot Integral

Calculus Level 5

This problem is flagged because the value of \(a, c\) isn't uniquely determined.

If the value of the integral \[\displaystyle \int\limits_{0}^{\infty} \frac{x^{n-1}}{x-1} dx = -\frac{a}{f(n)}\]

  1. \(0<n<1\)
  2. \(a \) is real
  3. \(f(n) \) is a real function of \( n \)
  4. \( f(0.125) = c \).

Find the value of \(a+\ln(c)\).

\(\blacksquare\) This is a part of Hot Integrals


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