逆2乗の別表示

\begin{align*} \frac{1}{(k+1)^{2}} & =\frac{1}{(k+1)}\int_{0}^{1}x^{k}dx\\ & =\frac{1}{(k+1)}\left(\left[x^{k+1}\log x\right]_{0}^{1}-\left(k+1\right)\int_{0}^{1}x^{k}\log xdx\right)\\ & =-\int_{0}^{1}x^{k}\log xdx \end{align*}