Consider the following example:
\documentclass{article}
\usepackage{amsmath, amsthm, amssymb, mathtools, thmtools, unicode-math}
\begin{document}
\begin{align*}
\hphantom{\Leftrightarrow}Lf&=0\\
\Leftrightarrow f''&=-\frac{2b}af'\\
\Leftrightarrow f'&=c_1\exp\left(-2\int_0^{\;\cdot}\frac ba(x)\:{\rm d}x\right)\\
\Leftrightarrow f&=c_1\int_0^{\;\cdot}\exp\left(-2\int_0^y\frac ba(x)\:{\rm d}x\right)\:{\rm d}y+c_2
\end{align*}
\end{document}
The desired output is as follows:
How can I achieve the correct alignment? Basically, it is a matrix with four columns. The content of the first, second and fourth column should be left, right and left aligned, respectively. How can we do this?