Consider a 2-dimensional archimedian copula with generator $\psi$ and $\gamma:=\psi^{-1}$, i.e.
$$C(u,v)=\gamma(\psi(u)+\psi(v))$$
I want to show that $$\tau=1-\int_{0}^{\infty}t\gamma'(t)^2dt$$
I know how to show $$\tau=1+4\int_{0}^{1}\frac{\psi(t)}{\psi'(t)}dt$$ Can I use this somehow to show $\tau=1-\int_{0}^{\infty}t\gamma'(t)^ 2dt$? How? Or is it better to show it directly? Thanks!