[Maxima-bugs] [ maxima-Bugs-1901044 ] Integrating problem of (a*x + b)^n dx general format

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Bugs item #1901044, was opened at 2008-02-24 17:21
Message generated for change (Comment added) made by rtoy
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Category: Lisp Core - Integration
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Valer Gonda (valergonda)
Assigned to: Nobody/Anonymous (nobody)
Summary: Integrating problem of (a*x + b)^n dx general format 

Initial Comment:
When integrate a function of general format 
(a*x + b)^n dx
Maxima doesn't use the simplest formula.

In case of integrating (a*x + b)^n dx Maxima should use:

(a*x + b)^(n + 1)
――――――――――――――――   to calculate.
  a * (n + 1)

That is:
                          n + 1
⌠         n      (a∙x + b)
⌡(a∙x + b) dx = ―――――――――――――
                  a∙(n + 1)
                

For example:
                          4
⌠         3      (5∙x - 2)
⌡(5∙x - 2) dx = ―――――――――――
                     20

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>Comment By: Raymond Toy (rtoy)
Date: 2008-02-26 09:11

Message:
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Barton,

Evaluate his test integral:  integrate((5*x-2)^3,x);

The result is not (5*x-2)^4/20, but slightly different.

I don't consider this a problem.

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Comment By: Barton Willis (willisbl)
Date: 2008-02-26 08:10

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With 5.14.0, I get

(%i65) integrate((a*x + b)^n,x);
Is  n + 1   zero or nonzero? nonzero;
(%o65) (a*x+b)^(n+1)/(a*(n+1))

Isn't this the answer you wanted?


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Comment By: Valer Gonda (valergonda)
Date: 2008-02-24 17:26

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That is:
                          n + 1
⌠         n      (a∙x + b)
⌡(a∙x + b) dx = ――――――――――――――――
                  a∙(n + 1)


For example:
                          4
⌠         3      (5∙x - 2)
⌡(5∙x - 2) dx = ―――――――――――
                    20

----------------------------------------------------------------------

You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1901044&group_id=4933