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Merged
merged 1 commit into from
May 27, 2022
Merged

manualintegrate sqrt(a+b*x+c*x**2) #23530

merged 1 commit into from
May 27, 2022

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eagleoflqj
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@eagleoflqj eagleoflqj commented May 21, 2022 •
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References to other Issues or PRs

Fixes #23485
Fixes #11742

Brief description of what is fixed or changed

The rule of this kind of integrals is
$\int\sqrt{a+bx+cx^2}\mathrm{d}x$
$=x\sqrt{a+bx+cx^2}-\int x\mathrm{d}\sqrt{a+bx+cx^2}$
$=x\sqrt{a+bx+cx^2}-\int\frac{x(b+2cx)}{2\sqrt{a+bx+cx^2}}\mathrm{d}x$
$=x\sqrt{a+bx+cx^2}-\int\frac{2(a+bx+cx^2)-2a-bx}{2\sqrt{a+bx+cx^2}}\mathrm{d}x$
$=x\sqrt{a+bx+cx^2}-\int\sqrt{a+bx+cx^2}\mathrm{d}x+\frac{1}{2}\int\frac{2a+bx}{\sqrt{a+bx+cx^2}}\mathrm{d}x$
$=\frac{1}{2}x\sqrt{a+bx+cx^2}+\frac{1}{4}\int\frac{2a+bx}{\sqrt{a+bx+cx^2}}\mathrm{d}x$
This rule doesn't seem represent-able by existing rules, so I define a new rule for it.
Detailed steps should be provided in SymPy Beta after SymPy 1.11 is released.

Other comments

Release Notes

  • integrals
    • Support integrate(sqrt(a+bx+cx**2))

@eagleoflqj eagleoflqj requested a review from oscarbenjamin May 21, 2022 03:05
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sympy-bot commented May 21, 2022 •
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Hi, I am the SymPy bot (v167). I'm here to help you write a release notes entry. Please read the guide on how to write release notes.

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#### References to other Issues or PRs
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Fixes #23485
Fixes #11742
#### Brief description of what is fixed or changed
The rule of this kind of integrals is
$\int\sqrt{a+bx+cx^2}\mathrm{d}x$
$=x\sqrt{a+bx+cx^2}-\int x\mathrm{d}\sqrt{a+bx+cx^2}$
$=x\sqrt{a+bx+cx^2}-\int\frac{x(b+2cx)}{2\sqrt{a+bx+cx^2}}\mathrm{d}x$
$=x\sqrt{a+bx+cx^2}-\int\frac{2(a+bx+cx^2)-2a-bx}{2\sqrt{a+bx+cx^2}}\mathrm{d}x$
$=x\sqrt{a+bx+cx^2}-\int\sqrt{a+bx+cx^2}\mathrm{d}x+\frac{1}{2}\int\frac{2a+bx}{\sqrt{a+bx+cx^2}}\mathrm{d}x$
$=\frac{1}{2}x\sqrt{a+bx+cx^2}+\frac{1}{4}\int\frac{2a+bx}{\sqrt{a+bx+cx^2}}\mathrm{d}x$
This rule doesn't seem represent-able by existing rules, so I define a new rule for it.
Detailed steps should be provided in SymPy Beta after SymPy 1.11 is released. 
#### Other comments


#### Release Notes

<!-- Write the release notes for this release below between the BEGIN and END
statements. The basic format is a bulleted list with the name of the subpackage
and the release note for this PR. For example:

* solvers
  * Added a new solver for logarithmic equations.

* functions
  * Fixed a bug with log of integers.

or if no release note(s) should be included use:

NO ENTRY

See https://github.com/sympy/sympy/wiki/Writing-Release-Notes for more
information on how to write release notes. The bot will check your release
notes automatically to see if they are formatted correctly. -->

<!-- BEGIN RELEASE NOTES -->
* integrals
  * Support integrate(sqrt(a+bx+cx**2))

<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

@eagleoflqj eagleoflqj marked this pull request as draft May 21, 2022 04:08
@eagleoflqj eagleoflqj force-pushed the integrate_sqrt_quadratic branch from 19c5f87 to 309a3a3 Compare May 21, 2022 17:29
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Significantly changed benchmark results (PR vs master)



Significantly changed benchmark results (master vs previous release)


       before           after         ratio
     [77f1d79c]       [832c24fe]
     <sympy-1.10.1^0>                 
+         130±3ms          237±7ms     1.83  sum.TimeSum.time_doit



Full benchmark results can be found as artifacts in GitHub Actions

(click on checks at the top of the PR).

      		
    

  





        


            

            
            

              
            

        

      


      

            
  
  

    
  
    
    

  

  

  


    












      

  
          

  
  

  
      @eagleoflqj
  eagleoflqj


        marked this pull request as ready for review

    May 21, 2022 20:00    
    









      

  
      



  

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Wolfram alpha gives a result without any integral https://www.wolframalpha.com/input?i=integrate+sqrt%28a%2Bb*x%2Bc*x**2%29+dx


Other than that, the presented derivation seems correct to me and the changes in the code make sense, although I am not too familiar with manualintegrate`.

      		
    

  





        


            

            
            

              
            

        

      


      

            
  
  

    
  
    
    

  

  

  


    












      

  
        

  

      

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                  May 22, 2022
                
            
            
          


          



              
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                sympy/integrals/tests/test_integrals.py

          
        


      
          
  

    
      
    
    

          


              

              

            
                         x*sqrt(53225*x**2 - 66732*x + 23013)/2 - 16683*sqrt(53225*x**2 - 66732*x + 23013)/53225 + \

            
          

          


              

              

            
                         111576969*sqrt(2129)*asinh(53225*x/10563 - S(11122)/3521)/1133160250

            
          

          


              

              

            
                  assert integrate(sqrt(a+b*x+c*x**2), x) == b*sqrt(a + b*x + c*x**2)/(4*c) + x*sqrt(a + b*x + c*x**2)/2 + \

            
          

          


              

              

            
                         (2*a - b**2/(2*c))*log(b + 2*sqrt(c)*sqrt(a + b*x + c*x**2) + 2*c*x)/(4*sqrt(c))

            
          

    








  

    

        

        

  

    

        
    
    

  


      
          
  
      
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@ThePauliPrinciple

The context is, I supported $\int\frac{2a+bx}{\sqrt{a+bx+cx^2}}\mathrm{d}x$ at #23511, so you can see the result here equals to Wolfram Alpha.

    

  
  



    


        

      
  
  

    
  
    
    

  

  

  



          

      
    








    


  









  








  








      

  
          
 
  

    
  

  



        @eagleoflqj
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        merged commit 109ea40
      into

      
  
    sympy:master
  


    May 27, 2022

  







  

  
  

  
      @eagleoflqj
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    deleted the
    
      
        integrate_sqrt_quadratic
    
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    May 27, 2022 17:34    
    













  
  

    

      

  




      


    


    

      

        
      

  
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                Awaiting requested review from oscarbenjamin


        
      


      






    

  


      
  

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Successfully merging this pull request may close these issues.



  
          
      integrate(sqrt(53225*t**2 - 66732*t + 23013), t) fails to integrate

  
          
      integrate cannot solve integral, but Meijer int can



  
  



      
    

  




      

    

  
      

  

    

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