Evaluate $\int_0^{\infty}\frac{\log( x)}{x^2+a^2} \,dx$ using contour integration; Re a > 0

Question

Evaluate $\int_0^{\infty}\frac{\log( x)}{x^2+a^2} \,dx$ using contour integration; $Re (a) > 0$

I found two questions where a > 0 but in my case I have the following condition: Re a > 0 (It seems like $a$ can be complex). What will be the difference in solutions?

Same questions:

Evaluate $\int_0^{\infty} \frac{\log(x)dx}{x^2+a^2}$ using contour integration

Contour integration of $\frac{\log( x)}{x^2+a^2}$

I tried to find residues of $\int_0^{\infty}\frac{\log^2( x)}{x^2+a^2} \,dx$ in z=$\pm$ia, where a-complex