Finding the definite integral $\int_0^1 \log x\,\mathrm dx$ $$\int_{0}^1 \log x \,\mathrm dx$$
How to solve this? I am having problems with the limit $0$ to $1$. Because $\log 0$ is undefined.

for every 's' we know that $ \int_{0}^{1}dxx^{s}=\frac{1}{1+s}$
take the derivative with respec to 's' at $ s=0 $ so $ \int_{0}^{1}dxlogx=-\frac{1}{(1+0)^{2}}=-1$
