Enumerated list of displayed integration questions

Question

How do I format a list of questions like this?

I'm getting the equation on a new line below the i) when using enumerate and \list. I don't want to get rid of \[ and \] either, as I like the long integral sign. I get this instead:

Answer 1

You can use \displaystyle to switch to the long integral:

\documentclass{article}

\begin{document}

\begin{enumerate}
\item $\displaystyle \int\frac{2+x}{(1+x)^2}\mathrm{d}x$.

\item $\displaystyle \int\frac{2x^2}{1-x^2}\mathrm{d}x$.
\end{enumerate}

\end{document}

Result:

Answer 2

For numbered equations you should use like this you should use the align environment from the amsmath package.

For the lowercase roman letters instead of the arabic ones you can either use the following to enable it for the whole document

\renewcommand{\theequation}{\roman{equation}}

… or use a counter which you increment after every line and use the tag command—something like this (then you can also use align* which doesn't do numbering by default):

\newcounter{eq}
\setcounter{eq}{0}

\begin{align}
    ... \tag{\text{\roman{eq}}}\stepcounter{eq}\\
    ... \tag{\text{\roman{eq}}}\stepcounter{eq}\\
    ... \tag{\text{\roman{eq}}}
\end{align}

To get the equation numbers on the left, you have to add leqno to your document class options.

At the end there might be

\documentclass[leqno]{article}
\usepackage{amsmath}
\renewcommand{\theequation}{\roman{equation}}
...
\begin{document}
    \begin{align}
        \int^\pi_0\frac{x\sin x}{3+\sin^2 x}\text{d}x\ \text{;}\\
        \int^{2\pi}_0\frac{x\sin x}{3+\sin^2 x}\text{d}x\ \text{;}\\
        \int^\pi_0\frac{x|\sin x|}{3+\sin^2 x}\text{d}x\ \text{.}
    \end{align}    
\end{document}