In the book Partial Diferential Equations by A. Friedman 1969. Part 2 on page 104, in the proof of theorem 2.1 (d).

A is a operator of type $(\psi,M)$ ($-A$generate a analytic semigroup), and $\Gamma$ is a smooth curve lying in the resolvent set of $-A$, $\lambda\in C$, the integrand $\frac{1}{2\pi i}\int_{\Gamma}(\lambda I+A)^{-1}Ax\frac{d\lambda}{\lambda}=0$, why? How to compute?

Thanks for any hint.