T18 级数 边界情况

$$\int \ln x\mathrm{d}x=x\ln x-x+C$$ $$\begin{gathered} g^{\prime }(x)=\sum _{n=1}^{\infty }\frac{x^n}{n}=-\ln (1-x) \\ g(x)-g(0)={\int }_0^x-\ln (1-t)\mathrm{d}t=(1-x)\ln (1-x)+x \end{gathered}$$