Otdfbt

If I want to copy block as latex I do copy as LaTeX. But when I write:

WolframAlpha["integrate (sin(x))^4 dx"]

How can I copy step by step solution as latex?

content = WolframAlpha["integrate (sin(x))^4 dx", "IndefiniteIntegral", 2, "Content",
 PodStates -> "IndefiniteIntegral__Step-by-step solution"][[1]];

BoxForm`$UseTemplateSlotSequenceForRow = False;

TeXForm[Column@(MakeExpression[content //. StyleBox[a_, ___] :> a, 
 StandardForm] /. a_, b_, c___ :> Column[HoldForm[a], HoldForm[b, c]], 
 r_Row :> HoldForm[r])[[1, All, 1]]]

$smallbeginarrayl
beginarrayl
textTake the integral: \
int sin ^4(x) , dx \
endarray
\
beginarrayl
textUse textthe textreduction textformula, int sin ^m(x) , dx
text= -fraccos (x) sin ^m-1(x)m text+ fracm-1mint sin
^-2+m(x) , dx, textwhere m=4: \
text= -frac14 sin ^3(x) cos (x)+frac34 int sin ^2(x) , dx \
endarray
\
beginarrayl
textWrite sin ^2(x) textas frac12-frac12 cos (2 x): \
text= -frac14 sin ^3(x) cos (x)+frac34 int
left(frac12-frac12 cos (2 x)right) , dx \
endarray
\
beginarrayl
textIntegrate textthe textsum textterm textby textterm textand
textfactor textout textconstants: \
text= -frac14 sin ^3(x) cos (x)-frac38 int cos (2 x) ,
dx+frac3 int 1 , dx8 \
endarray
\
beginarrayl
textFor textthe textintegrand cos (2 x), textsubstitute u=2 x
textand du=2, dx: \
text= -frac14 sin ^3(x) cos (x)-frac316 int cos (u) ,
du+frac3 int 1 , dx8 \
endarray
\
beginarrayl
textThe textintegral textof cos (u) textis sin (u): \
text= -frac116 (3 sin (u))-frac14 sin ^3(x) cos (x)+frac3 int
1 , dx8 \
endarray
\
beginarrayl
textThe textintegral textof 1 textis x: \
text= left(-frac116 (3 sin (u))+frac3 x8-frac14 sin ^3(x)
cos (x)right)+textconstant \
endarray
\
beginarrayl
textSubstitute textback textfor u=2 x: \
text= left(frac3 x8-frac14 sin ^3(x) cos (x)-frac38 sin (x)
cos (x)right)+textconstant \
endarray
\
beginarrayl
textWhich textis textequal textto: \
fbox$left(
beginarraycc
textAnswer: & \
text & text= frac132 (12 x-8 sin (2 x)+sin (4 x))+textconstant \
endarray
right)$ \
endarray
\
endarray$

You can just apply TeXForm to the content returned by WolframAlpha, although you will encounter 3 issues:

1. Some of the StyleBoxes use options that TeXForm doesn't recognize. TeXForm will issue messages and ignore them, so you can either use Quiet or strip out those options.




2. The TeXForm produced has empty lines. This causes problems for the MathJax engine.




3. Some spaces get removed.

So, one could do the following:

content = WolframAlpha[
 "integrate (sin(x))^4 dx",
 "IndefiniteIntegral",2,"Content",
 PodStates->"IndefiniteIntegral__Step-by-step solution"
];

StringReplace[Quiet @ ToString[content, TeXForm], "n" ~~ Whitespace ~~ "n" -> "n"]

which will fix the first 2 issues above. However, it is also possible to fix the internal code. The 3 specific problems with the internal code:

1. Some spaces need to have a text wrapper so that they don't disapper.


2. The internal code has a bug when Style uses lists of options.


3. The internal code tosses in some superfluous carriage returns ("n") that break MathJax.

I will provide code to fix these issues at the bottom of my answer. After running that code, simply using TeXForm produces the desired output:

TeXForm @ WolframAlpha[
 "integrate (sin(x))^4 dx",
 "IndefiniteIntegral",2,"Content",
 PodStates->"IndefiniteIntegral__Step-by-step solution"
]

$beginarrayl
beginarrayl
textTake the integral: \
int sin ^4(x) , dx \
endarray
\
hline
beginarrayl
textUse textthe textreduction textformula, int sin ^m(x) , dxtext text= -fraccos (x) sin ^m-1(x)mtext text+
fracm-1mint sin ^-2+m(x) , dx,text textwhere m=4: \
text text= -frac14 sin ^3(x) cos (x)+frac34int sin ^2(x) , dx \
endarray
\
beginarrayl
textWrite sin ^2(x)text textas frac12-frac12 cos (2 x): \
text text= -frac14 sin ^3(x) cos (x)+frac34int left(frac12-frac12 cos (2 x)right) , dx \
endarray
\
beginarrayl
textIntegrate textthe textsum textterm textby textterm textand textfactor textout textconstants: \
text text= -frac14 sin ^3(x) cos (x)-frac38int cos (2 x) , dx+frac38int 1 , dx \
endarray
\
beginarrayl
textFor textthe textintegrand cos (2 x),text textsubstitute u=2 xtext textand du=2, dx: \
text text= -frac14 sin ^3(x) cos (x)-frac316int cos (u) , du+frac38int 1 , dx \
endarray
\
beginarrayl
textThe textintegral textof cos (u)text textis sin (u): \
text text= -frac3 sin (u)16-frac14 sin ^3(x) cos (x)+frac38int 1 , dx \
endarray
\
beginarrayl
textThe textintegral textof 1text textis x: \
text text= -frac3 sin (u)16+frac3 x8-frac14 sin ^3(x) cos (x)+textconstant \
endarray
\
beginarrayl
textSubstitute textback textfor u=2 x: \
text text= frac3 x8-frac14 sin ^3(x) cos (x)-frac38 sin (x) cos (x)+textconstant \
endarray
\
beginarrayl
textWhich textis textequal textto: \
fbox$beginarrayll
textAnswer: & \
text & text text= frac132 (12 x-8 sin (2 x)+sin (4 x))+textconstant \
endarray
$ \
endarray
\
endarray$

As a comparison with kglr's answer, there is no need to use MakeExpression, no spurious parentheses get introduced (his answer has spurious parentheses in the "Answer" box), the spacing issue gets fixed (note the missing space in the line "the integral of 1is x:"), and the output is correct even when a step-by-step solution has only 1 step.

Now, for the code. Note that the usual caveats apply to the following code, which modifies the internal code used by Mathematica:

(* force autoloading of TeXForm code *)
TeXForm 

(* the following modification just flattens out options *)
System`Convert`TeXFormDump`maketex[(StyleBox|Cell)[System`Convert`CommonDump`str_,System`Convert`CommonDump`sty_String:"",System`Convert`CommonDump`opts__?OptionQ]] := Module[
 System`Convert`TeXFormDump`fv,System`Convert`TeXFormDump`und,System`Convert`TeXFormDump`fw,System`Convert`TeXFormDump`fs,System`Convert`CommonDump`pre="",System`Convert`CommonDump`post="",System`Convert`TeXFormDump`mid,
 System`Convert`TeXFormDump`fv=FontVariations/. Flatten@System`Convert`CommonDump`opts/. FontVariations->;
 System`Convert`TeXFormDump`und="Underline"/. System`Convert`TeXFormDump`fv/. "Underline"->False;
 System`Convert`TeXFormDump`fw,System`Convert`TeXFormDump`fs=FontWeight,FontSlant/. Flatten@System`Convert`CommonDump`opts/. FontWeight;
 System`Convert`TeXFormDump`mid=System`Convert`TeXFormDump`MakeTeX[StyleBox[System`Convert`CommonDump`str,System`Convert`CommonDump`sty]];
 If[System`Convert`TeXFormDump`fs==="Italic",System`Convert`TeXFormDump`mid=If[StringMatchQ[System`Convert`TeXFormDump`mid,"\text*"],StringTake[System`Convert`TeXFormDump`mid,7,-2],"$"<>System`Convert`TeXFormDump`mid<>"$"];System`Convert`CommonDump`pre="\text\textit"<>System`Convert`CommonDump`pre;System`Convert`CommonDump`post=System`Convert`CommonDump`post<>"";];
 If[System`Convert`TeXFormDump`und,System`Convert`CommonDump`pre="\underline"<>System`Convert`CommonDump`pre;System`Convert`CommonDump`post=System`Convert`CommonDump`post<>"";];
 If[System`Convert`TeXFormDump`fw==="Bold",System`Convert`CommonDump`pre="\pmb"<>System`Convert`CommonDump`pre;System`Convert`CommonDump`post=System`Convert`CommonDump`post<>"";];
 System`Convert`CommonDump`pre<>System`Convert`TeXFormDump`mid<>System`Convert`CommonDump`post
]

(* the following modification just removes the initial "n" *)
System`Convert`TeXFormDump`maketex[GridBox[System`Convert`TeXFormDump`grid_,System`Convert`CommonDump`opts___?OptionQ]] := Module[
 System`Convert`TeXFormDump`colaln,System`Convert`TeXFormDump`rowdivs,System`Convert`TeXFormDump`outstr,System`Convert`TeXFormDump`i,System`Convert`TeXFormDump`cols,System`Convert`TeXFormDump`rows,
 System`Convert`CommonDump`DebugPrint["------------------------------------"];
 System`Convert`CommonDump`DebugPrint["maketex[GridBox[grid_, opts___?OptionQ]]"];
 System`Convert`CommonDump`DebugPrint["grid: ",System`Convert`TeXFormDump`grid];
 System`Convert`TeXFormDump`cols=Dimensions[System`Convert`TeXFormDump`grid][[2]];
 System`Convert`TeXFormDump`rows=Dimensions[System`Convert`TeXFormDump`grid][[1]];
 System`Convert`TeXFormDump`colaln=System`Convert`TeXFormDump`processColumnOptions[System`Convert`CommonDump`opts,System`Convert`TeXFormDump`cols];
 System`Convert`TeXFormDump`rowdivs=System`Convert`TeXFormDump`processRowOptions[System`Convert`CommonDump`opts,System`Convert`TeXFormDump`rows];
 System`Convert`TeXFormDump`outstr="\beginarray"<>System`Convert`TeXFormDump`colaln<>""<>"n";
 For[System`Convert`TeXFormDump`i=1,System`Convert`TeXFormDump`i<=System`Convert`TeXFormDump`rows,System`Convert`TeXFormDump`i++,If[System`Convert`TeXFormDump`rowdivs[[System`Convert`TeXFormDump`i]]==True,System`Convert`TeXFormDump`outstr=System`Convert`TeXFormDump`outstr<>"\hline"<>"n"];System`Convert`TeXFormDump`outstr=System`Convert`TeXFormDump`outstr<>System`Convert`TeXFormDump`MakeRow[System`Convert`TeXFormDump`grid[[System`Convert`TeXFormDump`i]]];];
 If[Last[System`Convert`TeXFormDump`rowdivs]==True,System`Convert`TeXFormDump`outstr=System`Convert`TeXFormDump`outstr<>"\hline"<>"n"];
 System`Convert`TeXFormDump`outstr=System`Convert`TeXFormDump`outstr<>"\endarray"<>"n";
 System`Convert`TeXFormDump`outstr
]

(* The following modification prevents some spaces from getting lost *)
System`Convert`TeXFormDump`maketex["" ""] = "\text "

I tried to do this before, I could not find an option.

Alternative is to use "Plaintext" option, then copy the plain text to your latex editor and do some (lots) of manually clean up and editing

r = WolframAlpha[
 "Integrate[x Sin[x],x,0,Pi]", "Input", 2, "Plaintext", 
 PodStates -> "Input__Step-by-step solution"]

gives

Compute the definite integral:
 integral_0^[Pi] x sin(x) dx
For the integrand x sin(x), integrate by parts, integral f dg = f g - integral g df, where 
 f = x, dg = sin(x) dx, df = dx, g = -cos(x):
 = (-x cos(x)) right bracketing bar _0^[Pi] + integral_0^[Pi] cos(x) dx
Evaluate the antiderivative at the limits and subtract.
 (-x cos(x)) right bracketing bar _0^[Pi] = (-[Pi] cos([Pi])) - (-0 cos(0)) = [Pi]:
 = [Pi] + integral_0^[Pi] cos(x) dx
Apply the fundamental theorem of calculus.
The antiderivative of cos(x) is sin(x):
 = [Pi] + sin(x) right bracketing bar _0^[Pi]
Evaluate the antiderivative at the limits and subtract.
 sin(x) right bracketing bar _0^[Pi] = sin([Pi]) - sin(0) = 0:
Answer: | 
 | = [Pi]

Then clean it to become

documentclassarticle
usepackageamsmath
begin document

Compute the definite integral:
 $int_0^pi x sin(x) ,dx$

For the integrand $x sin(x)$, integrate by parts, $int f dg = f g - int g df$, where 
 $f = x, dg = sin(x) dx, df = dx, g = -cos(x) = (-x cos(x))$

Evaluate the antiderivative at the limits and subtract. etc...

end document

When done cleaning it by hand, compile it

I could not find a "TeXForm" option to Wolfram Alpha output.

[See here][1]: not $LaTeX$ but a good start:

WolframAlpha["integrate (sin(x))^4 dx", "PodPlaintext", 
 PodStates -> "IndefiniteIntegral__Step-by-step solution"]

 = 1/32 (12 x - 8 sin(2 x) + sin(4 x)) + constant", "(3 x)/8 + 1/8 
sin(x) cos^3(x) - 1/8 sin^3(x) cos(x) - 1/2 sin(x) cos(x) + 
constant", "(3 x)/8 - 1/8 i e^(-2 i x) + 1/8 i e^(2 i x) + 1/64 i 
e^(-4 i x) - 1/64 i e^(4 i x) + constant", "(3 x)/8 - 1/4 sin(2 x) + 
1/32 sin(4 x) + constant", "x^5/5 - (2 x^7)/21 + x^9/45 - (34 
x^11)/10395 + O(x^13)
 (Taylor series)", "integral_0^π sin^4(x) dx = (3 π)/8
≈1.1781", "integral_0^(2 π) sin^4(x) dx = (3 π)/4
≈2.35619", "integral_0^(2 π) (sin^8(x))/(2 π) dx 
= 35/128≈0.273438"```