% documentclass[fleqn]{article}
documentclass{exam}
usepackage{amsmath,mathtools}

DeclareMathOperator{ad}{ad}
DeclarePairedDelimiterabs{lvert}{rvert}

begin{document}
[
int_{a}^{b}f(x)dx=F(b)-F(a)
]
[
int_{a}^{b}f(x)dx=F(x)bigg|_{a}^{b}=F(b)-F(a)
]
[
e^{X}Ye^{-X}=e^{ad_{X}}Y=Y+[X,Y]+frac{1}{2!}[X,[X,Y]]+frac{1}{3!}[X,[X,[X,Y]]]+dots
]
[
hat{D}(alpha)=e^{-frac{1}{2}abs{alpha}^{2}}e^{+alphahat{a}^{dagger}}e^{-alpha^{*}hat{a}}=e^{+frac{1}{2}abs{alpha}^{2}}e^{-alpha^{*}hat{a}}e^{+alphahat{a}^{dagger}}
]
end{document}