=∫[0,+∞)(t/β+c)*β^α/γ(α)*(t/β)^(α- 1)*e^(-t)* 1/β*dt
= 1/γ(α)*∫[0,+∞){t^[(α+ 1)- 1]/β+ct^(α- 1)}e^(-t)dt
= 1/γ(α)*[ 1/β*γ(α+ 1)+cγ(α)]
= 1/γ(α)*[α/β*γ(α)+cγ(α)]
=α/β+c