Ggtkuk

I want to make a comment box like the image below that adjusts in size as I write up different examples. My MWE is not much

documentclassarticle
usepackageamsmath, mathtools,tikz

begindocument

beginalign* 
displaystyleint 3x^2(x^3+1)^10 dx &=int (textcolorred 
 x^3+1)^10 textcolorblue3x^2 dx \
 &=int textcolorredu^10 
 textcolorbluedu
endalign*

enddocument

This outputs:

I am trying to recreate with a black box drawn around the orange shaded area.

Using tikzmark, it is not so difficult:

documentclassarticle
usepackageamsmath, mathtools,tikz
usetikzlibrarytikzmark,calc
begindocument

beginalign* 
displaystyleint 3x^2(x^3+1)^10 dx &=int (textcolorred x^3+1)^10 textcolorblue3x^2 dx tikzmarkeqt\
&=int textcolorredu^10textcolorbluedu
endalign*

begintikzpicture[overlay, remember picture]
coordinate (x) at ($(pic cs:eqt)+(1,0)$);
draw (x)--($(x)+(3,0)$);
draw[red] (x) node[above right] Substitution;
draw ($(x)+(3,0)$) node[right,draw,fill=orange!50] % 
% Remove `draw' option if you don't want the box
$beginaligned
 u&=x^3+1,\
 du&=3x^2dx
endaligned$;
endtikzpicture

enddocument

This very nice and creative solution is by @marmot:

documentclass[fleqn]article
usepackageamsmath,tikz
usetikzlibrarytikzmark
begindocument

beginalign* 
displaystyleint 3x^2(x^3+1)^10,mathrmdx 
&tikzmarknodeeq1=int (textcolorred x^3+1)^10 
textcolorblue3x^2, mathrmdx \
&tikzmarknodeeq2=int textcolorredu^10,textcolorbluemathrmdu
endalign*

begintikzpicture[overlay, remember picture]
path (eq1) -- (eq2) coordinate[midway] (aux);
draw[latex-] (eq2) -- (aux) -- ++ (5,0) node[above left] substitute
node[right,fill=orange!30] %
$beginaligned
 u&=x^3+1\
 mathrmdu&=3x^2,mathrmdx
endaligned$;
endtikzpicture
enddocument

Without tikz, I define an extensible xmathline, centred on the math axis, which accepts writing above and below it, like xrightarrow, and add a simple colorbox:

documentclass[svgnames]article
usepackageamsmath, mathtools,tikz
usepackagexcolor
usepackagebigstrut

 newcommandxmathline[2][]%
 ext@arrow 0099xmathlinefill@#1#2%
 newcommandxmathlinefill@%
 arrowfill@relbarbigstrutrelbarrelbar
 makeatother

begindocument

beginalign*
displaystyleint 3x^2(x^3+1)^10 dx &=int (textcolorred
 x^3+1)^10 textcolorblue3x^2 dx
 quadxmathlinetextcolorCrimsonsubstitutionquadcolorboxNavajoWhite! 60$beginaligned u & = x^3 + 1 \ du & =3x^2,dx endaligned $ \%
 &=int textcolorredu^10
 textcolorbluedu
endalign*

enddocument