Calculate $$\int_0^1\frac{\ln(1+x)\ln(1-x)}{1+x}\,dx$$
My try :
Let : $$I(a,b)=\int_0^1\frac{\ln(1-ax)\ln(1+bx)}{1+x}\,dx$$
Then compute $\frac{d^2 I(a,b)}{dadb}$.
I'm happy to see ideas in order to kill this integral.
Calculate $$\int_0^1\frac{\ln(1+x)\ln(1-x)}{1+x}\,dx$$
My try :
Let : $$I(a,b)=\int_0^1\frac{\ln(1-ax)\ln(1+bx)}{1+x}\,dx$$
Then compute $\frac{d^2 I(a,b)}{dadb}$.
I'm happy to see ideas in order to kill this integral.