Integral with fraction and square root produces wrong vertical alignment

Question

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}

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
I still do not get what is awkward here? Do you refer to the integral sign having a smaller height than the fraction? — TeXnician, Dec 30 '18 at 16:20
The "!" commands were not intended to be left in the code, I was trying to improve the spacing in some way and then forgot to remove them, so you can just ignore them. — Lele99_DD, Dec 30 '18 at 16:25
If it was not for the negative spaces and the non-upright differential d, I'd agree with @egreg. — , Dec 30 '18 at 16:42
marmot the question you linked was exactly what I wanted, thanks — Lele99_DD, Dec 30 '18 at 16:48

score 7 · Accepted Answer · answered Dec 30 '18 at 16:43

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}

score 2 · Answer 2 · answered Dec 30 '18 at 16:57

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.

Lele99_DD · Answer 3 · 2018-12-30T17:14:59.923

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}

Integral with fraction and square root produces wrong vertical alignment

3 Answers3