Yep.

The integral with exp(-z/2) poses no problem whatsoever
for a human or Maple/Mathematica :) as it obviously boils
down to the exponential integral.

> int((1-exp(-z))*exp(-z/2)/z, z);
-Ei(1,1/2*z)+Ei(1,3/2*z)
 
> int((1-exp(-z))*exp(-z/2)/z, z=0..infinity);
ln(3)


No challenge.