How to calculate the integral $I=\int\limits_0^1\frac{x^n-1}{\ln(x)} \,\mathrm dx$ How can we calculate this integral:

$$I=\int\limits_0^1\frac{x^n-1}{\ln(x)}\,\mathrm dx$$

I believe that integral is equal to $\ln(n+1)$, but I don't lnow how to prove it.

Hint: $(a^x)'=a^x\cdot log(a)$
