What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$? /A problem from the 2012 MIT Integration Bee is
$$
\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx
$$
The answer is $\log(8)$. Wolfram Alpha gives an indefinite form in terms of the logarithmic integral function, but times out doing the computation. Is there a way to do it by hand?


Application of Leibniz's rule for integration
