## [Maxima-bugs] [ maxima-Bugs-1479149 ] Integration with trigonometric function and following diff

 [Maxima-bugs] [ maxima-Bugs-1479149 ] Integration with trigonometric function and following diff From: SourceForge.net - 2006-04-30 11:55:46 ```Bugs item #1479149, was opened at 2006-04-29 21:13 Message generated for change (Comment added) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1479149&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 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: Integration with trigonometric function and following diff Initial Comment: integrate(k*x/f(x),x), k-number, f(x)-thrigonometric function - sin(x)^2, cos(x)^2, Sin(x)^3 etc. gives a very poor result. axiom gives a better and short result. following diff(%,x) gives a non simply formula. So, maxima has a problem with a trigonometric function ;) ---------------------------------------------------------------------- >Comment By: Barton Willis (willisbl) Date: 2006-04-30 06:55 Message: Logged In: YES user_id=895922 Did Maxima give an incorrect result for any of these integrals? Maxima does gives a lengthy formula for integrate(x / sin(x)^2,x), but it seems to be correct: (%i1) integrate(x / sin(x)^2,x)\$ (%i2) diff(%,x) - x/sin(x)^2\$ (%i3) exponentialize(%)\$ (%i4) ratsimp(%); (%o4) 0 In addition to exponentialize and ratsimp, Maxima has functions trigsimp, trigreduce, and trigexpand. Did you try using these functions to convert the antiderivatives into the form you were looking for? Barton ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1479149&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-1479149 ] Integration with trigonometric function and following diff From: SourceForge.net - 2006-04-30 02:13:58 ```Bugs item #1479149, was opened at 2006-04-29 19:13 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=1479149&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 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: Integration with trigonometric function and following diff Initial Comment: integrate(k*x/f(x),x), k-number, f(x)-thrigonometric function - sin(x)^2, cos(x)^2, Sin(x)^3 etc. gives a very poor result. axiom gives a better and short result. following diff(%,x) gives a non simply formula. So, maxima has a problem with a trigonometric function ;) ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1479149&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1479149 ] Integration with trigonometric function and following diff From: SourceForge.net - 2006-04-30 11:55:46 ```Bugs item #1479149, was opened at 2006-04-29 21:13 Message generated for change (Comment added) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1479149&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 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: Integration with trigonometric function and following diff Initial Comment: integrate(k*x/f(x),x), k-number, f(x)-thrigonometric function - sin(x)^2, cos(x)^2, Sin(x)^3 etc. gives a very poor result. axiom gives a better and short result. following diff(%,x) gives a non simply formula. So, maxima has a problem with a trigonometric function ;) ---------------------------------------------------------------------- >Comment By: Barton Willis (willisbl) Date: 2006-04-30 06:55 Message: Logged In: YES user_id=895922 Did Maxima give an incorrect result for any of these integrals? Maxima does gives a lengthy formula for integrate(x / sin(x)^2,x), but it seems to be correct: (%i1) integrate(x / sin(x)^2,x)\$ (%i2) diff(%,x) - x/sin(x)^2\$ (%i3) exponentialize(%)\$ (%i4) ratsimp(%); (%o4) 0 In addition to exponentialize and ratsimp, Maxima has functions trigsimp, trigreduce, and trigexpand. Did you try using these functions to convert the antiderivatives into the form you were looking for? Barton ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1479149&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1479149 ] Integration with trigonometric function and following diff From: SourceForge.net - 2006-05-01 13:19:59 ```Bugs item #1479149, was opened at 2006-04-29 19:13 Message generated for change (Comment added) made by nobody You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1479149&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 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: Integration with trigonometric function and following diff Initial Comment: integrate(k*x/f(x),x), k-number, f(x)-thrigonometric function - sin(x)^2, cos(x)^2, Sin(x)^3 etc. gives a very poor result. axiom gives a better and short result. following diff(%,x) gives a non simply formula. So, maxima has a problem with a trigonometric function ;) ---------------------------------------------------------------------- Comment By: Nobody/Anonymous (nobody) Date: 2006-05-01 06:19 Message: Logged In: NO Yes, trigsimp was help me, it gives simpler, but not simplest formula. For example, k=2, f(x)=sin(x)^2 integrate(2*x/(sin(x)^2,x) with trigsimp gives a following formula: [{(cos(2x)-1)*log(2*cos(x)+2)}+{(cos(2*x)-1)*log(2-2*cos(x))}+2*x*sin(2*x)]/(cos(2*x)-1) Simplest result is: 2*(log(sin(x)/2)-x*ctg(x)) Or, maxima don't gives (don't can) a simplest result? P.S. By the way, how about C? integrate(x,x) = x^2/2 + C. doble integrate gives a x^3/6 + C*x + c(1) ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2006-04-30 04:55 Message: Logged In: YES user_id=895922 Did Maxima give an incorrect result for any of these integrals? Maxima does gives a lengthy formula for integrate(x / sin(x)^2,x), but it seems to be correct: (%i1) integrate(x / sin(x)^2,x)\$ (%i2) diff(%,x) - x/sin(x)^2\$ (%i3) exponentialize(%)\$ (%i4) ratsimp(%); (%o4) 0 In addition to exponentialize and ratsimp, Maxima has functions trigsimp, trigreduce, and trigexpand. Did you try using these functions to convert the antiderivatives into the form you were looking for? Barton ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1479149&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1479149 ] Integration with trigonometric function and following diff From: SourceForge.net - 2006-05-01 16:54:51 ```Bugs item #1479149, was opened at 2006-04-29 22:13 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1479149&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 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: Integration with trigonometric function and following diff Initial Comment: integrate(k*x/f(x),x), k-number, f(x)-thrigonometric function - sin(x)^2, cos(x)^2, Sin(x)^3 etc. gives a very poor result. axiom gives a better and short result. following diff(%,x) gives a non simply formula. So, maxima has a problem with a trigonometric function ;) ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2006-05-01 12:54 Message: Logged In: YES user_id=28849 Judicious use of logcontract, trigexpand and trigsimp will produce log(4-4*cos(x)^2)-2*x*cos(x)/sin(x). That's pretty comparable to axiom's result. Also, integrate never returns a gratuitious constant of integration, just like tables of integrals never do If you want it, you have to add it yourself. ---------------------------------------------------------------------- Comment By: Nobody/Anonymous (nobody) Date: 2006-05-01 09:19 Message: Logged In: NO Yes, trigsimp was help me, it gives simpler, but not simplest formula. For example, k=2, f(x)=sin(x)^2 integrate(2*x/(sin(x)^2,x) with trigsimp gives a following formula: [{(cos(2x)-1)*log(2*cos(x)+2)}+{(cos(2*x)-1)*log(2-2*cos(x))}+2*x*sin(2*x)]/(cos(2*x)-1) Simplest result is: 2*(log(sin(x)/2)-x*ctg(x)) Or, maxima don't gives (don't can) a simplest result? P.S. By the way, how about C? integrate(x,x) = x^2/2 + C. doble integrate gives a x^3/6 + C*x + c(1) ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2006-04-30 07:55 Message: Logged In: YES user_id=895922 Did Maxima give an incorrect result for any of these integrals? Maxima does gives a lengthy formula for integrate(x / sin(x)^2,x), but it seems to be correct: (%i1) integrate(x / sin(x)^2,x)\$ (%i2) diff(%,x) - x/sin(x)^2\$ (%i3) exponentialize(%)\$ (%i4) ratsimp(%); (%o4) 0 In addition to exponentialize and ratsimp, Maxima has functions trigsimp, trigreduce, and trigexpand. Did you try using these functions to convert the antiderivatives into the form you were looking for? Barton ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1479149&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1479149 ] Integration with trigonometric function and following diff From: SourceForge.net - 2006-05-01 17:04:47 ```Bugs item #1479149, was opened at 2006-04-29 21:13 Message generated for change (Comment added) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1479149&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 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: Integration with trigonometric function and following diff Initial Comment: integrate(k*x/f(x),x), k-number, f(x)-thrigonometric function - sin(x)^2, cos(x)^2, Sin(x)^3 etc. gives a very poor result. axiom gives a better and short result. following diff(%,x) gives a non simply formula. So, maxima has a problem with a trigonometric function ;) ---------------------------------------------------------------------- >Comment By: Barton Willis (willisbl) Date: 2006-05-01 12:04 Message: Logged In: YES user_id=895922 Maxima uses a constant of integration when it thinks one is really needed: (%i12) integrate(x=1,x); (%o12) x^2/2=x+integrationconstant1 This is a bug list--for a better place to ask questions about how to use Maxima see: http://maxima.sourceforge.net/maximalist.html Barton ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-05-01 11:54 Message: Logged In: YES user_id=28849 Judicious use of logcontract, trigexpand and trigsimp will produce log(4-4*cos(x)^2)-2*x*cos(x)/sin(x). That's pretty comparable to axiom's result. Also, integrate never returns a gratuitious constant of integration, just like tables of integrals never do If you want it, you have to add it yourself. ---------------------------------------------------------------------- Comment By: Nobody/Anonymous (nobody) Date: 2006-05-01 08:19 Message: Logged In: NO Yes, trigsimp was help me, it gives simpler, but not simplest formula. For example, k=2, f(x)=sin(x)^2 integrate(2*x/(sin(x)^2,x) with trigsimp gives a following formula: [{(cos(2x)-1)*log(2*cos(x)+2)}+{(cos(2*x)-1)*log(2-2*cos(x))}+2*x*sin(2*x)]/(cos(2*x)-1) Simplest result is: 2*(log(sin(x)/2)-x*ctg(x)) Or, maxima don't gives (don't can) a simplest result? P.S. By the way, how about C? integrate(x,x) = x^2/2 + C. doble integrate gives a x^3/6 + C*x + c(1) ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2006-04-30 06:55 Message: Logged In: YES user_id=895922 Did Maxima give an incorrect result for any of these integrals? Maxima does gives a lengthy formula for integrate(x / sin(x)^2,x), but it seems to be correct: (%i1) integrate(x / sin(x)^2,x)\$ (%i2) diff(%,x) - x/sin(x)^2\$ (%i3) exponentialize(%)\$ (%i4) ratsimp(%); (%o4) 0 In addition to exponentialize and ratsimp, Maxima has functions trigsimp, trigreduce, and trigexpand. Did you try using these functions to convert the antiderivatives into the form you were looking for? Barton ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1479149&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1479149 ] Integration with trigonometric function and following diff From: SourceForge.net - 2006-05-13 21:27:39 ```Bugs item #1479149, was opened at 2006-04-29 21:13 Message generated for change (Comment added) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1479149&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: Closed Resolution: None Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: Integration with trigonometric function and following diff Initial Comment: integrate(k*x/f(x),x), k-number, f(x)-thrigonometric function - sin(x)^2, cos(x)^2, Sin(x)^3 etc. gives a very poor result. axiom gives a better and short result. following diff(%,x) gives a non simply formula. So, maxima has a problem with a trigonometric function ;) ---------------------------------------------------------------------- >Comment By: Barton Willis (willisbl) Date: 2006-05-13 16:27 Message: Logged In: YES user_id=895922 No real bug here--I'm closing the report. Barton ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2006-05-01 12:04 Message: Logged In: YES user_id=895922 Maxima uses a constant of integration when it thinks one is really needed: (%i12) integrate(x=1,x); (%o12) x^2/2=x+integrationconstant1 This is a bug list--for a better place to ask questions about how to use Maxima see: http://maxima.sourceforge.net/maximalist.html Barton ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-05-01 11:54 Message: Logged In: YES user_id=28849 Judicious use of logcontract, trigexpand and trigsimp will produce log(4-4*cos(x)^2)-2*x*cos(x)/sin(x). That's pretty comparable to axiom's result. Also, integrate never returns a gratuitious constant of integration, just like tables of integrals never do If you want it, you have to add it yourself. ---------------------------------------------------------------------- Comment By: Nobody/Anonymous (nobody) Date: 2006-05-01 08:19 Message: Logged In: NO Yes, trigsimp was help me, it gives simpler, but not simplest formula. For example, k=2, f(x)=sin(x)^2 integrate(2*x/(sin(x)^2,x) with trigsimp gives a following formula: [{(cos(2x)-1)*log(2*cos(x)+2)}+{(cos(2*x)-1)*log(2-2*cos(x))}+2*x*sin(2*x)]/(cos(2*x)-1) Simplest result is: 2*(log(sin(x)/2)-x*ctg(x)) Or, maxima don't gives (don't can) a simplest result? P.S. By the way, how about C? integrate(x,x) = x^2/2 + C. doble integrate gives a x^3/6 + C*x + c(1) ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2006-04-30 06:55 Message: Logged In: YES user_id=895922 Did Maxima give an incorrect result for any of these integrals? Maxima does gives a lengthy formula for integrate(x / sin(x)^2,x), but it seems to be correct: (%i1) integrate(x / sin(x)^2,x)\$ (%i2) diff(%,x) - x/sin(x)^2\$ (%i3) exponentialize(%)\$ (%i4) ratsimp(%); (%o4) 0 In addition to exponentialize and ratsimp, Maxima has functions trigsimp, trigreduce, and trigexpand. Did you try using these functions to convert the antiderivatives into the form you were looking for? Barton ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1479149&group_id=4933 ```