## maxima-bugs

 [Maxima-bugs] [ maxima-Bugs-1901044 ] Integrating problem of (a*x + b)^n dx general format From: SourceForge.net - 2008-02-24 22:21:44 ```Bugs item #1901044, was opened at 2008-02-24 23:21 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1901044&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. 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 ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1901044&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1901044 ] Integrating problem of (a*x + b)^n dx general format From: SourceForge.net - 2008-02-24 22:26:59 ```Bugs item #1901044, was opened at 2008-02-24 23:21 Message generated for change (Comment added) made by valergonda You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1901044&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. 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 ---------------------------------------------------------------------- >Comment By: Valer Gonda (valergonda) Date: 2008-02-24 23:26 Message: Logged In: YES user_id=2018483 Originator: YES 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 ```
 [Maxima-bugs] [ maxima-Bugs-1901044 ] Integrating problem of (a*x + b)^n dx general format From: SourceForge.net - 2008-02-26 13:10:13 ```Bugs item #1901044, was opened at 2008-02-24 16:21 Message generated for change (Comment added) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1901044&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. 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 ---------------------------------------------------------------------- >Comment By: Barton Willis (willisbl) Date: 2008-02-26 07:10 Message: Logged In: YES user_id=895922 Originator: NO 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? ---------------------------------------------------------------------- Comment By: Valer Gonda (valergonda) Date: 2008-02-24 16:26 Message: Logged In: YES user_id=2018483 Originator: YES 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 ```
 [Maxima-bugs] [ maxima-Bugs-1901044 ] Integrating problem of (a*x + b)^n dx general format From: SourceForge.net - 2008-02-26 14:11:54 ```Bugs item #1901044, was opened at 2008-02-24 17:21 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1901044&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. 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 ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2008-02-26 09:11 Message: Logged In: YES user_id=28849 Originator: NO 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. ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2008-02-26 08:10 Message: Logged In: YES user_id=895922 Originator: NO 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? ---------------------------------------------------------------------- Comment By: Valer Gonda (valergonda) Date: 2008-02-24 17:26 Message: Logged In: YES user_id=2018483 Originator: YES 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 ```
 [Maxima-bugs] [ maxima-Bugs-1901044 ] Integrating problem of (a*x + b)^n dx general format From: SourceForge.net - 2008-02-26 14:24:10 ```Bugs item #1901044, was opened at 2008-02-24 16:21 Message generated for change (Comment added) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1901044&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. 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 ---------------------------------------------------------------------- >Comment By: Barton Willis (willisbl) Date: 2008-02-26 08:24 Message: Logged In: YES user_id=895922 Originator: NO Oh, okay -- we have (%i1) integrate((5*x-2)^199,x); (%o1) (5*x-2)^200/1000 (%i2) integrate((5*x-2)^3,x); (%o2) (125*x^4)/4-50*x^3+30*x^2-8*x Is there an option variable that controls the expansion of the integrand / antiderivative? ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2008-02-26 08:11 Message: Logged In: YES user_id=28849 Originator: NO 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. ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2008-02-26 07:10 Message: Logged In: YES user_id=895922 Originator: NO 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? ---------------------------------------------------------------------- Comment By: Valer Gonda (valergonda) Date: 2008-02-24 16:26 Message: Logged In: YES user_id=2018483 Originator: YES 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 ```
 [Maxima-bugs] [ maxima-Bugs-1901044 ] Integrating problem of (a*x + b)^n dx general format From: SourceForge.net - 2008-02-26 14:40:39 ```Bugs item #1901044, was opened at 2008-02-24 17:21 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1901044&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. 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 ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2008-02-26 09:40 Message: Logged In: YES user_id=28849 Originator: NO Ah, found it. Look in diffdiv in src/sin.lisp. The first clause of the cond expression checks to see if the exponent is between 0 and 6 (exclusive). If so, it expands out the expression and integrates again. If not, it tries some other approach. Of course, there are no comments on why it does this and why 6. ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2008-02-26 09:24 Message: Logged In: YES user_id=895922 Originator: NO Oh, okay -- we have (%i1) integrate((5*x-2)^199,x); (%o1) (5*x-2)^200/1000 (%i2) integrate((5*x-2)^3,x); (%o2) (125*x^4)/4-50*x^3+30*x^2-8*x Is there an option variable that controls the expansion of the integrand / antiderivative? ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2008-02-26 09:11 Message: Logged In: YES user_id=28849 Originator: NO 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. ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2008-02-26 08:10 Message: Logged In: YES user_id=895922 Originator: NO 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? ---------------------------------------------------------------------- Comment By: Valer Gonda (valergonda) Date: 2008-02-24 17:26 Message: Logged In: YES user_id=2018483 Originator: YES 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 ```