[Tex/LaTex] How to 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}