assume(gamma>0);

Cauchy(x,gamma) := gamma/(%pi∗(x∗∗2+gamma∗∗2));

assume(alpha>0);

assume(alpha<1);

h(x,y,alpha) := (x∗y)/((1-alpha)∗y+alpha∗x);

assume(gamma1>0);

assume(gamma2>0);

m(x,alpha) := ratsimp(h(Cauchy(x,gamma1),Cauchy(x,gamma2),alpha));

/∗ calculate Z ∗/

integrate(m(x,alpha),x,-inf,inf);