# Awkward spacing for integral in exponent

I'm trying to put an integral in an exponent with the following LaTeX:

\begin{align*}
e^{G(t)} &= e^{\int{\frac{t}{1+t^2}dt}} \\
&= e^{\frac{1}{2}\ln(1+t^2)} \\
&= \sqrt{1 + t^2}
\end{align*}


however, the result is this: the spacing between the integral and the fraction looks very awkward. I looked into display mode, but that just makes the integral abnormally large. Is there anyway to get rid of that spacing?

• I found this: tex.stackexchange.com/q/233817/120578, this: latex.org/forum/viewtopic.php?t=10000 and this: stackoverflow.com/questions/1437423/… on this particular problem... Jan 20, 2018 at 0:52
• As an aside, \int{...} doesn't really make sense: \int is just a symbol (technically a \mathop), it doesn't take arguments. Jan 20, 2018 at 0:53
• @koleygr Ah, I did searches specifically for integrals in exponents, but maybe it would've been smarter for me to search more generally... Jan 20, 2018 at 0:54
• @BrunoLeFloch Yeah, I just thought the spacing could possibly go away with the \int{...} but I was wrong Jan 20, 2018 at 0:55

Some alternatives:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{align*}
e^{G(t)} &= e^{\int\frac{t}{1+t^2}dt} \\ % original
e^{G(t)} &= e^{\int\!\frac{t}{1+t^2}\,dt} \\
e^{G(t)} &= \exp\Bigl(\int\frac{t}{1+t^2}\,dt\Bigr) \\
e^{G(t)} &= \exp\bigl({\textstyle\int\frac{t}{1+t^2}\,dt}\bigr) \\
&= e^{\frac{1}{2}\ln(1+t^2)} \\
&= \sqrt{1 + t^2}
\end{align*}

\end{document} • The \! seems to move it enough to not annoy me, thank you! Unrelated, is \exp an acceptable alternative to e^n? I've never seen that notation before. Jan 20, 2018 at 0:59
• @ryanyz10: \exp(...) for e^{...} is quite standard.
– GuM
Jan 20, 2018 at 1:19

Does this befit you?

\documentclass{article}
\usepackage{mathtools, graphicx}

\begin{document}

\begin{align*}
e^{G(t)} &= e^{\int{\mkern-7mu\frac{t}{1+t^{\scalebox{0.8}{$\scriptscriptstyle2$}}} dt}} \\
&= e^{\frac{1}{2}\ln(1+t^2)} \\
&= \sqrt{1 + t^2}
\end{align*}

\end{document} • @Mico: thanks. Still I hope my proposition is not totally unworthy :–) Jan 20, 2018 at 2:24
• I like either anwers of Bernard and egreg. I vote always your answer. Too for Mico and marmot. +1. Jan 20, 2018 at 8:14