# 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

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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