mathbot Feature: Step by step solutions

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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    id='MSP6227185ba9226487e03500005534f25c7f5690h1'
    host='https://www5a.wolframalpha.com'
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    related='https://www5a.wolframalpha.com/api/v1/relatedQueries.jsp?id=MSPa6228185ba9226487e03500001ecg2hc0g7afb47f3773634836471742935'
    version='2.6'
    inputstring='integral x^3 ln^2 x dx'>
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     scanner='Integral'
     id='IndefiniteIntegral'
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   <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'
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   <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'
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   <img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP6232185ba9226487e03500002g128g6cea8c7894?MSPStoreType=image/gif&amp;s=42'
       alt='Plots of the integral'
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       alt='Plots of the integral'
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       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'
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       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'
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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'
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       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'
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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