Align operators inside big brackets - using alignat*

Question

The obvious alignment would be the = and the + signs, however, I do wish to align the es). alignat* allows me to alternate between right and left alignment, so I can have right alignment before the es and left alignment after the es.

However, the es are enclosed by big ∫ brackets, and the alignment prohibits the compiler to realise that the closing brackets is associated with the opening brackets.

MWE

\documentclass{article}
\usepackage{mathtools}
\begin{document}

\[ F(s) = \mathcal{L}\{f(t)\} = \int_{0}^{\infty} f(t)e^{-st} dt \]

\begin{alignat*}{8}
             F(s)
 &&=        \int_{0}^{1}      1\cdot &e^{-st} dt  
  &+        \int_{1}^{2}     -1\cdot &e^{-st} dt  
  &+        \int_{2}^{\infty} 0\cdot &e^{-st} dt\\
 &&= \left[-\tfrac{1}{s}\cdot &e^{-st}\right]_{0}^{1}
  &+ \left[ \tfrac{1}{s}\cdot &e^{-st}\right]_{1}^{2}
  &+ \left[                 0 &       \right]_{2}^{\infty}
\end{alignat*}

\end{document}

Answer 1

I'm not sure this is a good idea, anyway here's how you can do it.

The trick is remembering that alignat (here in the internal version alignedat) makes pairs of right- and left-aligned columns.

A few {} are needed to ensure correct spacing around binary operation symbols.

\documentclass{article}
\usepackage{mathtools}
\begin{document}

\begin{gather*}
F(s) = \mathcal{L}\{f(t)\} = \int_{0}^{\infty} f(t)e^{-st}\,dt
\\
\begin{alignedat}{8}
F(s)
&=  & \int_{0}^{1}      1 &\cdot{}&& e^{-st}\,dt &
&+{}& \int_{1}^{2}     -1 &\cdot{}&& e^{-st}\,dt &
&+{}& \int_{2}^{\infty}{} & 0 \cdot e^{-st}\,dt
\\
&=  & \Bigl[-\frac{1}{s} &\cdot{}&& e^{-st}\Bigr]_{0}^{1} &
&+{}& \Bigl[ \frac{1}{s} &\cdot{}&& e^{-st}\Bigr]_{1}^{2} &
&+{}& \Bigl[&0\Bigr]_{2}^{\infty}
\end{alignedat}
\end{gather*}

\end{document}

Avoiding the repetition:

\documentclass{article}
\usepackage{mathtools}
\begin{document}

\begin{align*}
F(s) &= \mathcal{L}\{f(t)\} = \int_{0}^{\infty} f(t)e^{-st}\,dt
\\
&\begin{alignedat}{8}
&=  & \int_{0}^{1}      1 &\cdot{}&& e^{-st}\,dt &
&+{}& \int_{1}^{2}     -1 &\cdot{}&& e^{-st}\,dt &
&+{}& \int_{2}^{\infty}{} & 0 \cdot e^{-st}\,dt
\\
&=  & \Bigl[-\frac{1}{s} &\cdot{}&& e^{-st}\Bigr]_{0}^{1} &
&+{}& \Bigl[ \frac{1}{s} &\cdot{}&& e^{-st}\Bigr]_{1}^{2} &
&+{}& \Bigl[&0\Bigr]_{2}^{\infty}
\end{alignedat}
\end{align*}

\end{document}

My preference would go to the following setting, because I start from the idea that readers can read.

\documentclass{article}
\usepackage{mathtools}
\begin{document}

\begin{align*}
F(s) &= \mathcal{L}\{f(t)\} = \int_{0}^{\infty} f(t)e^{-st}\,dt
\\
     &= \int_{0}^{1}  1\cdot e^{-st}\,dt
      + \int_{1}^{2} -1\cdot e^{-st}\,dt
      + \int_{2}^{\infty} 0\cdot e^{-st}\,dt
\\
&= \Bigl[-\frac{1}{s} e^{-st}\Bigr]_{0}^{1}
 + \Bigl[ \frac{1}{s} e^{-st}\Bigr]_{1}^{2}
 + \Bigl[0\Bigr]_{2}^{\infty}
\end{align*}

\end{document}