## [Maxima-bugs] [ maxima-Bugs-3405408 ] integrate bug

 [Maxima-bugs] [ maxima-Bugs-3405408 ] integrate bug From: SourceForge.net - 2011-09-07 10:11:16 ```Bugs item #3405408, was opened at 2011-09-07 12:31 Message generated for change (Comment added) made by aleksasd You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3405408&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: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Aleksas (aleksasd) Assigned to: Nobody/Anonymous (nobody) Summary: integrate bug Initial Comment: Wrong: (%i1) integrate(acos((x-1/2)/sqrt(1-x^2)),x); (%o1) -(%pi*x)/2 The result should be (%i2) sol:(2^(3/2)*x*acos((2*x-1)/(2*sqrt(1-x^2))) -sqrt(2)*asin((10*x+1)/(2*sqrt(7)*(x+1))) +sqrt(2)*asin((6*x-5)/(2*sqrt(7)*(x-1))) +asin((4*x-1)/sqrt(7)))/2^(3/2)\$ Test of sol: (%i3) f:acos((x-1/2)/sqrt(1-x^2))\$ (%i4) diff(sol,x)-f,radcan; (%o4) 0 (%i5) is(%=0); (%o5) true Next a detailed solution has bug: (%i6) load(bypart)\$ (%i7) assume(abs(x)<1); (%o7) [abs(x)<1] (%i8) byparts(f,x,f,x),factor\$ (%i9) sol1:ev(%, nouns),factor\$ Test of sol1: (%i10) diff(sol1,x)-f,radcan\$ (%i11) is(%=0); (%o11) false Note: this integral is from http://www.math.utexas.edu/pipermail/maxima/2011/025866.html (%i12) S1:'integrate(acos((2*c+k*u)/sqrt((1-k^2/4)*(1-u^2))),u)\$ (%i13) subst([k=2/sqrt(5),c=-1/2/sqrt(5)],S1),factor; (%o13) integrate(acos((2*u-1)/(2*sqrt(1-u^2))),u) ---------------------------------------------------------------------- >Comment By: Aleksas (aleksasd) Date: 2011-09-07 13:11 Message: WolframAlpha solution of this problem is not correct. The result is undefined for x=0 (in real domain). ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3405408&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-2018888 ] integrate bug From: SourceForge.net - 2008-07-15 19:21:43 ```Bugs item #2018888, was opened at 2008-07-16 03:21 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=2018888&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: Chien Chang Shun (bagwe) Assigned to: Nobody/Anonymous (nobody) Summary: integrate bug Initial Comment: my maxima version is 5.15 (%i1) integrate(x*%e^(-x),x); (%o1) (-x - 1)*%e^(-x)<---wrong (-x + 1)*%e^(-x)<---correct ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2018888&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2018888 ] integrate bug From: SourceForge.net - 2008-07-15 20:51:27 ```Bugs item #2018888, was opened at 2008-07-15 15:21 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2018888&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: Chien Chang Shun (bagwe) Assigned to: Nobody/Anonymous (nobody) Summary: integrate bug Initial Comment: my maxima version is 5.15 (%i1) integrate(x*%e^(-x),x); (%o1) (-x - 1)*%e^(-x)<---wrong (-x + 1)*%e^(-x)<---correct ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2008-07-15 16:51 Message: Logged In: YES user_id=28849 Originator: NO Why do you think maxima is wrong? If I calculate the derivative of maxima's answer, I get the integrand again. If I do the same with your expected answer, I don't get the integrand. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2018888&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2018888 ] integrate bug From: SourceForge.net - 2008-07-16 06:31:07 ```Bugs item #2018888, was opened at 2008-07-16 03:21 Message generated for change (Comment added) made by bagwe You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2018888&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: Chien Chang Shun (bagwe) Assigned to: Nobody/Anonymous (nobody) Summary: integrate bug Initial Comment: my maxima version is 5.15 (%i1) integrate(x*%e^(-x),x); (%o1) (-x - 1)*%e^(-x)<---wrong (-x + 1)*%e^(-x)<---correct ---------------------------------------------------------------------- >Comment By: Chien Chang Shun (bagwe) Date: 2008-07-16 14:31 Message: Logged In: YES user_id=2053474 Originator: YES To rtoy: sorry,I am wrong!Maxima is right, How can I delete the this report? ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2008-07-16 04:51 Message: Logged In: YES user_id=28849 Originator: NO Why do you think maxima is wrong? If I calculate the derivative of maxima's answer, I get the integrand again. If I do the same with your expected answer, I don't get the integrand. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2018888&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2018888 ] integrate bug From: SourceForge.net - 2008-07-16 13:04:19 ```Bugs item #2018888, was opened at 2008-07-15 15:21 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2018888&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: Deleted >Resolution: Invalid Priority: 5 Private: No Submitted By: Chien Chang Shun (bagwe) Assigned to: Nobody/Anonymous (nobody) Summary: integrate bug Initial Comment: my maxima version is 5.15 (%i1) integrate(x*%e^(-x),x); (%o1) (-x - 1)*%e^(-x)<---wrong (-x + 1)*%e^(-x)<---correct ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2008-07-16 09:04 Message: Logged In: YES user_id=28849 Originator: NO Closing this bug. ---------------------------------------------------------------------- Comment By: Chien Chang Shun (bagwe) Date: 2008-07-16 02:31 Message: Logged In: YES user_id=2053474 Originator: YES To rtoy: sorry,I am wrong!Maxima is right, How can I delete the this report? ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2008-07-15 16:51 Message: Logged In: YES user_id=28849 Originator: NO Why do you think maxima is wrong? If I calculate the derivative of maxima's answer, I get the integrand again. If I do the same with your expected answer, I don't get the integrand. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2018888&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3405408 ] integrate bug From: SourceForge.net - 2011-09-07 09:31:25 ```Bugs item #3405408, was opened at 2011-09-07 12:31 Message generated for change (Tracker Item Submitted) made by aleksasd You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3405408&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: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Aleksas (aleksasd) Assigned to: Nobody/Anonymous (nobody) Summary: integrate bug Initial Comment: Wrong: (%i1) integrate(acos((x-1/2)/sqrt(1-x^2)),x); (%o1) -(%pi*x)/2 The result should be (%i2) sol:(2^(3/2)*x*acos((2*x-1)/(2*sqrt(1-x^2))) -sqrt(2)*asin((10*x+1)/(2*sqrt(7)*(x+1))) +sqrt(2)*asin((6*x-5)/(2*sqrt(7)*(x-1))) +asin((4*x-1)/sqrt(7)))/2^(3/2)\$ Test of sol: (%i3) f:acos((x-1/2)/sqrt(1-x^2))\$ (%i4) diff(sol,x)-f,radcan; (%o4) 0 (%i5) is(%=0); (%o5) true Next a detailed solution has bug: (%i6) load(bypart)\$ (%i7) assume(abs(x)<1); (%o7) [abs(x)<1] (%i8) byparts(f,x,f,x),factor\$ (%i9) sol1:ev(%, nouns),factor\$ Test of sol1: (%i10) diff(sol1,x)-f,radcan\$ (%i11) is(%=0); (%o11) false Note: this integral is from http://www.math.utexas.edu/pipermail/maxima/2011/025866.html (%i12) S1:'integrate(acos((2*c+k*u)/sqrt((1-k^2/4)*(1-u^2))),u)\$ (%i13) subst([k=2/sqrt(5),c=-1/2/sqrt(5)],S1),factor; (%o13) integrate(acos((2*u-1)/(2*sqrt(1-u^2))),u) ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3405408&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3405408 ] integrate bug From: SourceForge.net - 2011-09-07 10:11:16 ```Bugs item #3405408, was opened at 2011-09-07 12:31 Message generated for change (Comment added) made by aleksasd You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3405408&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: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Aleksas (aleksasd) Assigned to: Nobody/Anonymous (nobody) Summary: integrate bug Initial Comment: Wrong: (%i1) integrate(acos((x-1/2)/sqrt(1-x^2)),x); (%o1) -(%pi*x)/2 The result should be (%i2) sol:(2^(3/2)*x*acos((2*x-1)/(2*sqrt(1-x^2))) -sqrt(2)*asin((10*x+1)/(2*sqrt(7)*(x+1))) +sqrt(2)*asin((6*x-5)/(2*sqrt(7)*(x-1))) +asin((4*x-1)/sqrt(7)))/2^(3/2)\$ Test of sol: (%i3) f:acos((x-1/2)/sqrt(1-x^2))\$ (%i4) diff(sol,x)-f,radcan; (%o4) 0 (%i5) is(%=0); (%o5) true Next a detailed solution has bug: (%i6) load(bypart)\$ (%i7) assume(abs(x)<1); (%o7) [abs(x)<1] (%i8) byparts(f,x,f,x),factor\$ (%i9) sol1:ev(%, nouns),factor\$ Test of sol1: (%i10) diff(sol1,x)-f,radcan\$ (%i11) is(%=0); (%o11) false Note: this integral is from http://www.math.utexas.edu/pipermail/maxima/2011/025866.html (%i12) S1:'integrate(acos((2*c+k*u)/sqrt((1-k^2/4)*(1-u^2))),u)\$ (%i13) subst([k=2/sqrt(5),c=-1/2/sqrt(5)],S1),factor; (%o13) integrate(acos((2*u-1)/(2*sqrt(1-u^2))),u) ---------------------------------------------------------------------- >Comment By: Aleksas (aleksasd) Date: 2011-09-07 13:11 Message: WolframAlpha solution of this problem is not correct. The result is undefined for x=0 (in real domain). ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3405408&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3405408 ] integrate bug From: SourceForge.net - 2011-09-10 05:44:01 ```Bugs item #3405408, was opened at 2011-09-07 12:31 Message generated for change (Comment added) made by aleksasd You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3405408&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: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Aleksas (aleksasd) Assigned to: Nobody/Anonymous (nobody) Summary: integrate bug Initial Comment: Wrong: (%i1) integrate(acos((x-1/2)/sqrt(1-x^2)),x); (%o1) -(%pi*x)/2 The result should be (%i2) sol:(2^(3/2)*x*acos((2*x-1)/(2*sqrt(1-x^2))) -sqrt(2)*asin((10*x+1)/(2*sqrt(7)*(x+1))) +sqrt(2)*asin((6*x-5)/(2*sqrt(7)*(x-1))) +asin((4*x-1)/sqrt(7)))/2^(3/2)\$ Test of sol: (%i3) f:acos((x-1/2)/sqrt(1-x^2))\$ (%i4) diff(sol,x)-f,radcan; (%o4) 0 (%i5) is(%=0); (%o5) true Next a detailed solution has bug: (%i6) load(bypart)\$ (%i7) assume(abs(x)<1); (%o7) [abs(x)<1] (%i8) byparts(f,x,f,x),factor\$ (%i9) sol1:ev(%, nouns),factor\$ Test of sol1: (%i10) diff(sol1,x)-f,radcan\$ (%i11) is(%=0); (%o11) false Note: this integral is from http://www.math.utexas.edu/pipermail/maxima/2011/025866.html (%i12) S1:'integrate(acos((2*c+k*u)/sqrt((1-k^2/4)*(1-u^2))),u)\$ (%i13) subst([k=2/sqrt(5),c=-1/2/sqrt(5)],S1),factor; (%o13) integrate(acos((2*u-1)/(2*sqrt(1-u^2))),u) ---------------------------------------------------------------------- Comment By: Aleksas (aleksasd) Date: 2011-09-10 08:44 Message: Correct value of integrate(acos((x-1/2)/sqrt(1-x^2)),x) and "radcan" bug (%i1) f:acos((x-1/2)/sqrt(1-x^2))\$ (%i2) load(bypart)\$ (%i3) assume(abs(x)<1)\$ (%i4) byparts(f,x,f,1),factor\$ (%i5) sol2:ev(%, nouns),factor; (%o5) (2^(3/2)*x*acos((2*x-1)/(2*sqrt(1-x^2))) -sqrt(2)*asin((10*x+1)/(2*sqrt(7)*(x+1))) -sqrt(2)*asin((6*x-5)/(2*sqrt(7)*(x-1))) +asin((4*x-1)/sqrt(7)))/2^(3/2) Test of solution(the first method): (%i6) diff(sol2,x)-f\$ factor(%); (%o7) 0 (%i8) is(%=0); (%o8) true Test of solution(the second method): (%i9) diff(sol2,x)-f\$ radcan(%); (%o10) 1/((%i*x-%i)*sqrt(8*x^2-4*x-3)) (%i11) is(%=0); (%o11) false I think that solution sol2 is correct and "radcan" has bug (%i12) build_info()\$ Maxima version: 5.25.0 Maxima build date: 12:0 8/2/2011 Host type: i686-pc-mingw32 Lisp implementation type: Clozure Common Lisp Lisp implementation version: Version 1.7-r14925M (WindowsX8632) ---------------------------------------------------------------------- Comment By: Aleksas (aleksasd) Date: 2011-09-07 13:11 Message: WolframAlpha solution of this problem is not correct. The result is undefined for x=0 (in real domain). ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3405408&group_id=4933 ```