# Integral with fraction and square root produces wrong vertical alignment

This code produces an ankward vertical alignment which involves the integral symbol and the fraction with the square root at the denominator. Why? How can I fix this?

\documentclass[a4paper]{article}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}

\begin{document}
$\int_{x_0}^{x(t)} \! \! \! \frac{1}{\sqrt{\frac{2}{m}\bigl (E_0-V(x)\bigr)}} \, dx = t-t_0$
\end{document}

• What is awkward for you and how would you like it to look? – TeXnician Dec 30 '18 at 16:17
• I've also tried using the "bigints" package to get a bigger integral symbol, but it doesn't do the job, in fact the symbol won't get aligned properly anyway... Answering TeXnician: the integral symbol should be vertically aligned with the square root symbol at the denominator. – Lele99_DD Dec 30 '18 at 16:18
• Does any of the answers to this question help? – user121799 Dec 30 '18 at 16:34
• I see nothing strange. – egreg Dec 30 '18 at 16:36
• If it was not for the negative spaces and the non-upright differential d, I'd agree with @egreg. – user121799 Dec 30 '18 at 16:42

That's how it's supposed to be typeset.

Growing the integral symbol is out of the question, in my opinion. Moving it down is similarly disgraceful.

\documentclass[a4paper]{article}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}

\begin{document}

\noindent
No square root
$\int_{x_0}^{x(t)} \biggl(\frac{2}{m}\bigl(E_0-V(x)\bigr)\biggr)^{\!-1/2}\, dx = t-t_0$
Smashed square root
$\int_{x_0}^{x(t)} \frac{1}{\sqrt{\smash[b]{\frac{2}{m}}(E_0-V(x))}} \, dx = t-t_0$
Normal
$\int_{x_0}^{x(t)} \frac{1}{\sqrt{\frac{2}{m}\bigl(E_0-V(x)\bigr)}} \, dx = t-t_0$
\end{document}


I probably would do

\documentclass[a4paper]{article}
\usepackage{amsmath}

\begin{document}
$\int\limits_{x_0}^{x(t)} \frac{1}{\sqrt{\frac{2}{m}\bigl (E_0-V(\xi)\bigr)}} \, \mathrm{d}\xi = t-t_0$
\end{document}


to avoid confusion between the upper limit of the integral, x(t), and the integration variable as well between some quantity d (like a diameter, say) and the differential d. \int\limits makes the integral symbol look higher.

As marmot suggested, I tried using the scalerel package and I like the outcome. It's not perfect, but I think it's acceptable. The integral symbol is finally aligned with the bottom of the fraction.

\documentclass[a4paper]{article}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}

\usepackage{scalerel}

\begin{document}
\def\x{\frac{1}{\sqrt{\frac{2}{m}\bigl(E_0-V
(\xi)\bigr)}}}
${\scalerel*[2.2ex]{\int}{\x}}_{\!\!\!x_0}^{\,x(t)}\x\,\, d\xi \, = \, t-t_0$
\end{document}