What kind of integral is this?

Question

can anyone tell me what kind of package or what to type for getting an integral like this on the image, where the \frac{happines}{time} is below death? All the integrals I can find will push the frac to after death.

Answer 1

With the help of the bigints package (cf. Big integral sign), and some negative space, using Steven's code as a starting point.

\documentclass{article} 
\usepackage{bigints}
\begin{document}
\[
\mathit{Life} = \hspace{-0.8em} \bigint_{\mathit{birth}}^{\mathit{death}}\hspace{-2.5em}\frac{\mathit{happiness}}{\mathit{time}} \Delta \mathit{time}
\]
\end{document}

Answer 2

Using bigints is a good start. Negative kerning is then needed around the equality and before the fraction.

\documentclass{article}

\usepackage[osf]{Baskervaldx} % tosf in text, tlf in math
\usepackage[baskervaldx,vvarbb]{newtxmath}
\usepackage{bigints}

\begin{document}

\begin{displaymath}
  \textit{Life} \mkern-2mu = \mkern-18mu
  \bigints_{\textit{birth}}^{\textit{death}} \mkern-42mu
  \frac{\textit{happiness}}{\textit{time}} \,\Delta \textit{time}
\end{displaymath}

\end{document}

Answer 3

Here's a start.

\documentclass{article} 
\begin{document}
\[
\mathit{Life} = \int_\mathit{birth}^\mathit{death}\frac{\mathit{happiness}}{\mathit{time}} \Delta \mathit{time}
\]
\end{document}

More refined:

\documentclass{article} 
\usepackage{scalerel,mathtools}
\begin{document}
\[
\mathit{Life} {\,=} \!\!\!\!\vcenter{\hbox{%
  $\displaystyle{\scaleto[2em]{\int}{60pt}}_{%
    \mkern-27mu\mathit{birth}}^{\mathit{death}}$}}\mkern-44mu%
      \frac{\mathit{happiness}}{\mathit{time}}\,\Delta\,\mathit{time}
\]
\end{document}

Answer 4

Here's a solution that uses the mtpro2 package and its \XXL\int construct.

% !TeX program = pdflatex 
\documentclass{article}
\usepackage{mathtools,newtxtext}
\usepackage[lite]{mtpro2}
\begin{document}
\[
\textit{\Large Life}=\XXL\int_{\mathrlap{\textit{birth}}}^{\mathrlap{\textit{death}}}
  \mkern-15mu\frac{\textit{happiness}}{\textit{time}}\Delta\textit{time}
\]
\end{document}