I can't use & tabs in the `align` environment while using it inside a custom environment

Question

I've got a custom environment made for problem sets, and it uses a tabular to align the question number and question body. When I try to use & to group parts of an equation together - like if I want to align the = sign across multiple equations, I get compile errors. Is there any way I can fix this behavior? I'm all for getting rid of the tabular in my environment if I can use some other method to align the question body in a way that's visually equivalent to what I have now...

MWE:

\documentclass{article}

\RequirePackage{amsmath, amsthm}
\RequirePackage{thmtools}

\newcounter{problem}
\setcounter{problem}{0}

\newlength{\mylen}
\settowidth{\mylen}{100}

\newenvironment{problem}[1][]{%
  \refstepcounter{problem}
  \par\noindent
  \begin{tabular}{m{\mylen}p{\dimexpr\linewidth-\mylen-3\tabcolsep\relax}@{}}
  \arabic{problem}. & \ifx\relax#1\relax \else\textbf{#1}\\[1mm]&\fi
  }
  {\end{tabular}\ignorespacesafterend\medskip}%

\begin{document}
  \begin{problem}
    \begin{align*}
          =&\int_{1}^{3}\left(x+\frac{1}{x}\right)\ dx\\
          =&\left.\frac{1}{2}x^{2}+ln\lvert x\rvert\;\right|_{1}^{3}
    \end{align*}
  \end{problem}
\end{document}

Answer 1

Here's the solution that I got from somebody else while trying to fix another issue related to this badly designed environment. It had the effect of also fixing this issue.

I've included two extra environment definitions just to allow my example to work, since it was pulled from a homework assignment.

\documentclass{article}

\usepackage{mathtools}
\usepackage{amssymb}
\usepackage{enumitem}

\newcounter{problem}
\setcounter{problem}{0}

\newenvironment{problem}[1][]{
  \refstepcounter{problem}%
  \begin{list}{\arabic{problem}.}
              {\settowidth{\labelwidth}{100}%
               \setlength{\rightmargin}{0pt}%
              }
    \item \ifx\relax#1\relax \else\textbf{#1}\\[1mm]\fi
    }
    {\end{list}}

\newenvironment{parts}
  {\begin{enumerate}[label=\alph*)]}
  {\end{enumerate}}

\def\qed{\ensuremath{\square}} % <-QED Symbol
\newenvironment{solution}{%  <-Solution
  \par\addvspace{1em}
  \itshape{Solution:}\\}
  {\par\normalfont\hfill\qed\par\addvspace{\medskipamount}}%

\begin{document}
  \begin{problem}[Evaluate the integrals:]
    \begin{parts}
      \item $\displaystyle\int\sec^4{x}\ dx$
      \begin{solution}
        \begin{align*}
          \int\sec^2{x}\ dx&=\int\sec^2{x}\sec^2{x}\ dx\\
          &=\int\left(\tan^2{x}+1\right)\sec^2{x}\ dx\\
          &=\int\tan^2{x}\sec^2{x}\ dx+\int\sec^2{x}\ dx\\
          &=\frac{1}{3}\left[\tan^3{x}+3\tan{x}\right]+C
        \end{align*}
      \end{solution}
    \end{parts}
  \end{problem}
\end{document}

Answer 2

As proposed in my comment, here a solution (?) with enumitem.

The list qrr@problem is created with the label format \arabic*. (where * stands for the counter internally used).

The problem environment then uses the qrr@problem environment to automatically add the first (and in your case only) \item, either without or with the text given in the mandatory argument. (The optional first argument is forwarded to the qrr@problem list.)

Code

\documentclass{article}

\RequirePackage{amsmath, amsthm}
\RequirePackage{thmtools, enumitem}

\newlist{qrr@problem}{enumerate}{1}
\setlist[qrr@problem,1]{label=\arabic*.,resume}

\makeatletter
\newenvironment{problem}[2][]{%
    \qrr@problem[#1]\item\if\relax\detokenize{#2}\relax\relax\else\textbf{#2}\fi
}{%
    \endqrr@problem
}
\makeatother
\begin{document}
  \begin{problem}{}
    \begin{align*}
          y & = \int_{1}^{3}\left(x+\frac{1}{x}\right)\ dx\\
            & = \left.\frac{1}{2}x^{2}+ln\lvert x\rvert\;\right|_{1}^{3}
    \end{align*}
  \end{problem}

  \begin{problem}{Next problem, same equation}
    \begin{align*}
          y & = \int_{1}^{3}\left(x+\frac{1}{x}\right)\ dx \\
            & = \left.\frac{1}{2}x^{2}+ln\lvert x\rvert\;\right|_{1}^{3}
    \end{align*}
  \end{problem}
\end{document}

Output