Feature: Step by step solutions

[DenverCoder1]

Wolfram Alpha provides step by step solutions for some problems through their API.

This would be an extremely useful feature for this bot and it shouldn't be difficult to implement assuming you already use the WA API.

More details: https://products.wolframalpha.com/show-steps-api/documentation/

Example query: Note: it is required to pass an APIKEY (which I have removed for privacy)

https://api.wolframalpha.com/v2/query?appid=APIKEY&input=integral%20x^3%20ln^2%20x%20dx&podstate=Step-by-step%20solution&format=image

Query result

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<queryresult success='true'
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    recalculate=''
    id='MSP6227185ba9226487e03500005534f25c7f5690h1'
    host='https://www5a.wolframalpha.com'
    server='42'
    related='https://www5a.wolframalpha.com/api/v1/relatedQueries.jsp?id=MSPa6228185ba9226487e03500001ecg2hc0g7afb47f3773634836471742935'
    version='2.6'
    inputstring='integral x^3 ln^2 x dx'>
 <pod title='Indefinite integrals'
     scanner='Integral'
     id='IndefiniteIntegral'
     position='100'
     error='false'
     numsubpods='2'
     primary='true'>
  <subpod title=''>
   <img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP6229185ba9226487e03500004f6ia342d3595215?MSPStoreType=image/gif&amp;s=42'
       alt='integral x^3 log^2(x) dx = 1/32 x^4 (8 log^2(x) - 4 log(x) + 1) + constant'
       title='integral x^3 log^2(x) dx = 1/32 x^4 (8 log^2(x) - 4 log(x) + 1) + constant'
       width='403'
       height='38'
       type='Default'
       themes='1,2,3,4,5,6,7,8,9,10,11,12'
       colorinvertable='true' />
  </subpod>
  <subpod title='Possible intermediate steps'>
   <img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP6230185ba9226487e03500002b8b54i9604c3i4a?MSPStoreType=image/gif&amp;s=42'
       alt='Take the integral:
 integral x^3 log^2(x) dx
For the integrand x^3 log^2(x), integrate by parts, integral f dg = f g - integral g df, where 
 f = log^2(x), dg = x^3 dx, df = (2 log(x))/x dx, g = x^4/4:
 = 1/4 x^4 log^2(x) - 1/4 integral2 x^3 log(x) dx
Factor out constants:
 = 1/4 x^4 log^2(x) - 1/2 integral x^3 log(x) dx
For the integrand x^3 log(x), integrate by parts, integral f dg = f g - integral g df, where 
 f = log(x), dg = x^3 dx, df = 1/x dx, g = x^4/4:
 = -1/8 x^4 log(x) + 1/4 x^4 log^2(x) + 1/8 integral x^3 dx
The integral of x^3 is x^4/4:
 = x^4/32 + 1/4 x^4 log^2(x) - 1/8 x^4 log(x) + constant
Which is equal to:
Answer: | 
 | = 1/32 x^4 (8 log^2(x) - 4 log(x) + 1) + constant'
       title='Take the integral:
 integral x^3 log^2(x) dx
For the integrand x^3 log^2(x), integrate by parts, integral f dg = f g - integral g df, where 
 f = log^2(x), dg = x^3 dx, df = (2 log(x))/x dx, g = x^4/4:
 = 1/4 x^4 log^2(x) - 1/4 integral2 x^3 log(x) dx
Factor out constants:
 = 1/4 x^4 log^2(x) - 1/2 integral x^3 log(x) dx
For the integrand x^3 log(x), integrate by parts, integral f dg = f g - integral g df, where 
 f = log(x), dg = x^3 dx, df = 1/x dx, g = x^4/4:
 = -1/8 x^4 log(x) + 1/4 x^4 log^2(x) + 1/8 integral x^3 dx
The integral of x^3 is x^4/4:
 = x^4/32 + 1/4 x^4 log^2(x) - 1/8 x^4 log(x) + constant
Which is equal to:
Answer: | 
 | = 1/32 x^4 (8 log^2(x) - 4 log(x) + 1) + constant'
       width='524'
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       colorinvertable='true' />
   <infos count='1'>
    <info text='log(x) is the natural logarithm'>
     <img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP6231185ba9226487e0350000681d47e441725b11?MSPStoreType=image/gif&amp;s=42'
         alt='log(x) is the natural logarithm'
         title='log(x) is the natural logarithm'
         width='198'
         height='19' />
     <link url='http://reference.wolfram.com/language/ref/Log.html'
         text='Documentation'
         title='Mathematica' />
     <link url='http://functions.wolfram.com/ElementaryFunctions/Log'
         text='Properties'
         title='Wolfram Functions Site' />
     <link url='http://mathworld.wolfram.com/NaturalLogarithm.html'
         text='Definition'
         title='MathWorld' />
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 <pod title='Plots of the integral'
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     id='Plot'
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     error='false'
     numsubpods='2'>
  <subpod title=''>
   <img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP6232185ba9226487e03500002g128g6cea8c7894?MSPStoreType=image/gif&amp;s=42'
       alt='Plots of the integral'
       title=''
       width='335'
       height='134'
       type='2DMathPlot_1'
       themes='1,2,3,4,5,6,7,8,9,10,11,12'
       colorinvertable='true' />
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  <subpod title=''>
   <img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP6233185ba9226487e035000027cc6ig523diai4d?MSPStoreType=image/gif&amp;s=42'
       alt='Plots of the integral'
       title=''
       width='335'
       height='135'
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 <pod title='Alternate form of the integral'
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   <img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP6234185ba9226487e03500001050902e1ii63fea?MSPStoreType=image/gif&amp;s=42'
       alt='x^4 ((log^2(x))/4 - log(x)/8 + 1/32) + constant'
       title='x^4 ((log^2(x))/4 - log(x)/8 + 1/32) + constant'
       width='255'
       height='49'
       type='Default'
       themes='1,2,3,4,5,6,7,8,9,10,11,12'
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 <pod title='Expanded form of the integrals'
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   <img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP6235185ba9226487e035000052h887g2a766d42f?MSPStoreType=image/gif&amp;s=42'
       alt='x^4/32 + 1/4 x^4 log^2(x) - 1/8 x^4 log(x) + constant'
       title='x^4/32 + 1/4 x^4 log^2(x) - 1/8 x^4 log(x) + constant'
       width='285'
       height='43'
       type='Default'
       themes='1,2,3,4,5,6,7,8,9,10,11,12'
       colorinvertable='true' />
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  <subpod title='Possible intermediate steps'>
   <img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP6236185ba9226487e03500005d4ffa71b9ga81aa?MSPStoreType=image/gif&amp;s=42'
       alt='Expand the following:
(x^4 (1 - 4 log(x) + 8 log(x)^2))/32
x^4 (1 - 4 log(x) + 8 log(x)^2) = x^4×1 + x^4 (-4 log(x)) + x^4×8 log(x)^2:
(x^4 - 4 x^4 log(x) + 8 x^4 log(x)^2)/32
(x^4 - 4 x^4 log(x) + 8 x^4 log(x)^2)/32 = x^4/32 - (4 x^4 log(x))/32 + (8 x^4 log(x)^2)/32:
x^4/32 - (4 x^4 log(x))/32 + (8 x^4 log(x)^2)/32
The gcd of -4 and 32 is 4, so (-4 x^4 log(x))/32 = ((4 (-1)) x^4 log(x))/(4×8) = 4/4×(-x^4 log(x))/8 = (-x^4 log(x))/8:
x^4/32 + (-1 x^4 log(x))/8 + (8 x^4 log(x)^2)/32
8/32 = 8/(8×4) = 1/4:
Answer: | 
 | x^4/32 - (x^4 log(x))/8 + (x^4 log(x)^2)/4'
       title='Expand the following:
(x^4 (1 - 4 log(x) + 8 log(x)^2))/32
x^4 (1 - 4 log(x) + 8 log(x)^2) = x^4×1 + x^4 (-4 log(x)) + x^4×8 log(x)^2:
(x^4 - 4 x^4 log(x) + 8 x^4 log(x)^2)/32
(x^4 - 4 x^4 log(x) + 8 x^4 log(x)^2)/32 = x^4/32 - (4 x^4 log(x))/32 + (8 x^4 log(x)^2)/32:
x^4/32 - (4 x^4 log(x))/32 + (8 x^4 log(x)^2)/32
The gcd of -4 and 32 is 4, so (-4 x^4 log(x))/32 = ((4 (-1)) x^4 log(x))/(4×8) = 4/4×(-x^4 log(x))/8 = (-x^4 log(x))/8:
x^4/32 + (-1 x^4 log(x))/8 + (8 x^4 log(x)^2)/32
8/32 = 8/(8×4) = 1/4:
Answer: | 
 | x^4/32 - (x^4 log(x))/8 + (x^4 log(x)^2)/4'
       width='450'
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       type='Default'
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       colorinvertable='true' />
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     numsubpods='1'>
  <subpod title=''>
   <img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP6237185ba9226487e03500005g0baeieh53cd3c0?MSPStoreType=image/gif&amp;s=42'
       alt='integral_0^1 x^3 log^2(x) dx = 1/32 = 0.03125'
       title='integral_0^1 x^3 log^2(x) dx = 1/32 = 0.03125'
       width='224'
       height='38'
       type='Default'
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       colorinvertable='true' />
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The second link (https://www4b.wolframalpha.com/Calculate/MSP/MSP20411ebib521338c9a5800005h54e68eb6i7i8f4?MSPStoreType=image/gif&s=38) displays this image:

Example step by step image

If this could be implemented, that would be awesome.

Thanks!

[sonataop13]

Isn't the step-by-step API like $10K per year?

[DenverCoder1]

@sonataop13 Only after a certain amount of queries (which I assume a bot of this size probably would use up).

Maybe it can be made available for developers to enable if they are hosting it themselves?

That way if you only need a few queries per month, you can do it with your own API key?