4 (a) Sea $n$ un entero positivo. Calcule $\displaystyle \int_0^1 x^{n-1}\ln x\,dx$ . (b) Calcule $\displaystyle \sum_{n=0}^{\infty}(-1)^n\left(\frac{1}{(n+1)^2}-\frac{1}{(n+2)^2}+\frac{1}{(n+3)^2}-\dots \right).$