How can I make this equation fit on a single line?

Question

I want to make this equation fit on one line. I've tried to use \small, but it doesn't work. What should I do?

\begin{equation}
1^{st}integral= \int_{0}^{\infty}{\frac{2 \pi \zeta}{\alpha} t^{(\frac{-2}{\alpha}-1)}e^{- \pi t^{\frac{-2}{\alpha}} \sum_{i\in K}{\frac{\lambda_i P_i ^{\frac{2}{\alpha}} \rho(D_i\hat{T}_i,\alpha)}{D_i\hat{T}_i^{\frac{2}{\alpha}}}}}  e^{- \pi \zeta t^{\frac{-2}{\alpha}}}dt}
\nonumber  
\end{equation}

Answer 1

Multiplying the exponentials and factoring out a common expression makes this a little shorter, and perhaps a little easier to read.

If 2/\alpha (which appears five times in your expression) has semantic significance you could consider naming it, say \beta.

\documentclass[a4paper]{article}
\usepackage[showframe,margin=1in]{geometry}
\usepackage{amsmath}
\begin{document}

\begin{equation*}
\text{1\textsuperscript{st} integral} 
= \int_{0}^{\infty}
\frac{2 \pi \zeta}{\alpha} \, t^{(-2/\alpha-1)}
\exp\biggl(- \pi t^{-2/\alpha}
\biggl( \zeta + 
\sum_{i\in K}\frac{\lambda_i P_i ^{2/\alpha}
  \rho(D_i\hat{T}_i,\alpha)}{D_i\hat{T}_i^{2/\alpha}}
\biggr)
\biggr)  
\,dt 
\end{equation*}

\end{document}

Answer 2

When there's a trade-off between (a) minimizing the space taken up by a long and complicated expression, e.g., by making it fit on one line (and, in the process, making various subformulas so small as to make them hard to parse) and (b) maximizing good readability and parsability, I'd usually give extra weight to maintaining good readability.

Assuming your document has a fairly narrow text block, e.g., if its textwidth is that of a "standard" LaTeX article-class document, I think it's a good idea to break the formula across two lines, in part because it lets you enlarge the various arguments of the two exponential terms; see the first formula below. If, on the other hand, your paper size is either "A4" or (US) "Letter" and the margins are 1 inch (2.54 cm) wide, you needn't break the line at all even when using the larger display elements; see the second formula. (The thin horizontal and vertical lines are drawn by the showframe option of the geometry package.)

\documentclass[a4paper]{article}
\usepackage[showframe,margin=1in]{geometry}
\usepackage{amsmath}
\begin{document}

\begin{align*}
\text{1\textsuperscript{st} integral} 
&= \int_{0}^{\infty}
\frac{2 \pi \zeta}{\alpha} \, t^{(-2/\alpha-1)}\\
&\qquad \times \exp\biggl(- \pi t^{-2/\alpha} \sum_{i\in K}
\frac{\lambda_i P_i ^{2/\alpha} \rho(D_i\hat{T}_i,\alpha)}{D_i\hat{T}_i^{2/\alpha}}\biggr)  
\exp\Bigl(- \pi \zeta t^{-2/\alpha}\Bigr)\,dt 
\end{align*}

\begin{equation*}
\text{1\textsuperscript{st} integral} 
= \int_{0}^{\infty}
\frac{2 \pi \zeta}{\alpha} \, t^{(-2/\alpha-1)}
\exp\biggl(- \pi t^{-2/\alpha} \sum_{i\in K}
\frac{\lambda_i P_i ^{2/\alpha} \rho(D_i\hat{T}_i,\alpha)}{D_i\hat{T}_i^{2/\alpha}}\biggr)  
\exp\Bigl(- \pi \zeta t^{-2/\alpha}\Bigr)\,dt 
\end{equation*}
\end{document}