\documentclass[border=0 2]{standalone}
\usepackage{amsmath}
\begin{document}
$\displaystyle
\biggl(\int_{-\infty}^{\infty}e^{-x^2}\,dx\biggr)^{\!2}=
\biggl(\int_{-\infty}^{\infty}e^{-x^2}\,dx\biggr)
\biggl(\int_{-\infty}^{\infty}e^{-y^2}\,dy\biggr)=
\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-x^2-y^2}\,dx\,dy=
\int_{0}^{2\pi}\int_{0}^{\infty}e^{-\rho^2}\,\rho\,d\rho\,d\varphi=
\int_{0}^{2\pi}\biggl[-\frac{e^{-\rho^2}}{2}\biggr]_0^{\infty}\,d\varphi=
2\pi\cdot\frac{1}{2}=\pi
$
\end{document}