  This note addresses monotonic growths and logarithmic convexities of the
weighted ($(1-t^2)^\alpha dt^2$, $-\infty<\alpha<\infty$, $0<t<1$) integral
means $\mathsf{A}_{\alpha,\beta}(f,\cdot)$ and
$\mathsf{L}_{\alpha,\beta}(f,\cdot)$ of the mixed area $(\pi
r^2)^{-\beta}A(f,r)$ and the mixed length $(2\pi r)^{-\beta}L(f,r)$
($0\le\beta\le 1$ and $0<r<1$) of $f(r\mathbb D)$ and $\partial f(r\mathbb D)$
under a holomorphic map $f$ from the unit disk $\mathbb D$ into the finite
complex plane $\mathbb C$.
