Toggle between \dfrac and \tfrac in integrals

Question

I would like to learn how auto-program my document to display integrals with fractions nicely.

My MWE:

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

$\int_{\frac{1}{2}}^{\frac{\pi}{10}} \frac{x^2+x+1}{e^x +3}$ \vspace{1cm} %standard display

$\frac{x^2+x+1}{e^x+\frac{3}{2}}$ \vspace{1cm} %standard display 

\end{document}

What I would like to know is how do I program it so that if you have a limits with fractions use \tfrac for the limits but if you have a fraction on it own, use \dfrac.

Desired result:

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

$\displaystyle\int_{\tfrac{1}{2}}^{\tfrac{\pi}{10}} \dfrac{x^2+x+1}{e^x +3}$ \vspace{1cm} %uses \tfrac for limits and \dfrac for fraction

$\dfrac{x^2+x+1}{e^x+\frac{3}{2}}$ \vspace{1cm}  %uses \dfrac because its a fraction 

\end{document}

Answer 1

If you use mathematics environments (e.g. \begin{equation} ... \end{equation} from amsmath then most of the maths elements will be in display style but (as you may have noticed) the fractions in your integral limits will still be small (text-style).

The most straightforward approach I can think of is to define a custom command that has the integral `template' how you would like.

To achieve your integral with fractions in both limits, you could use the command (I've named it \intfrac) as \newcommand{\intfrac}[5]{\displaystyle\int_{\tfrac{#1}{#2}}^{\tfrac{#3}{#4}} #5 } which you would use (as per your MWE) as \intfrac{1}{2}{\pi}{10}{\frac{x^2+x+1}{e^x +3}} to achieve what you wish. This works both in-line and in a maths environment.

A downside is that this requires you to make a command for every 'instance' of fraction limits - like when only one limit is a fraction. So it's not the best solution, but it may work for you.

\documentclass{article}
\usepackage{amsmath}

\newcommand{\intfrac}[5]{\displaystyle\int_{\tfrac{#1}{#2}}^{\tfrac{#3}{#4}} #5 }

\begin{document}

% within environment. Notice typical answer has small fractions.
\begin{equation}
\intfrac{1}{2}{\pi}{10}{\frac{x^2+x+1}{e^x +3}}\\
\int_{\frac{1}{2}}^{\frac{\pi}{10}} \frac{x^2+x+1}{e^x +3}
\end{equation}

% in-line environment
$\intfrac{1}{2}{\pi}{10}{\frac{x^2+x+1}{e^x +3}}$

% from your MWE
$\displaystyle\int_{\tfrac{1}{2}}^{\tfrac{\pi}{10}} \frac{x^2+x+1}{e^x +3}$ \vspace{1cm} %uses \tfrac for limits and \dfrac for fraction

$\dfrac{x^2+x+1}{e^x+\frac{3}{2}}$ \vspace{1cm}  %uses \dfrac because its a fraction 

\end{document}

Answer 2

As far as I understand, the switch that you ask for is the standard behaviour of \frac using an inline (script) style in the limits and display style in the top level of display math

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

\[\int_{\frac{1}{2}}^{\frac{\pi}{10}} \frac{x^2+x+1}{e^x +3}\]



\[\frac{x^2+x+1}{e^x+\frac{3}{2}}\]

\end{document}