# 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
\[\displaystyle \int\limits_{0}^{\infty} \frac{x^{n-1}}{x-1} dx = -\frac{a}{f(n)}\]

where

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

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

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