$\int_{a}^{b}xe^{-m(x-t)^2} dx $
where m and t are constants,
ive tried solving this by ...
$\int_{a}^{b}xe^{-m(x-t)^2} dx $ = $\int_{a}^{b}(x-t)e^{-m(x-t)^2} dx $ + t$\int_{a}^{b}e^{-m(x-t)^2} dx $
substituting x-t = u and then
= $\int_{a-t}^{b-t}(u)e^{-m(u)^2} du $ + t$\int_{a-t}^{b-t}e^{-m(u)^2} du $
after that...
as $\int_{a-t}^{b-t}(u)e^{-m(u)^2} du $ = -1/2 $ \int_{a-t}^{b-t}(d/dm)e^{-m(u)^2} du $
not really sure where to go after that or am i on the wrong track???