$X$ and $Y$ are independent RVs, and given that the moment generating function of each: ${M_X(t)=e^{t^2+1}}$ and $M_Y(t)=e^{t-1}$. So the mgf of $2X+3Y$ should be $M_{2X+3Y}(t)=e^{4t^2+3t}$, and thus I can get the mean of the sum from the mgf.
$E[2X+3Y]=3$, but when I calculate $E[X]$ and $E[Y]$ using their own mgf and add them together following the law of linearity of $E$, I get the result $E[2X+3Y]=3/e$. I don't know if there is something wrong with my calculation or I have misunderstood some concepts.