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From: SourceForge.net <noreply@so...>  20110907 10:11:16

Bugs item #3405408, was opened at 20110907 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((x1/2)/sqrt(1x^2)),x); (%o1) (%pi*x)/2 The result should be (%i2) sol:(2^(3/2)*x*acos((2*x1)/(2*sqrt(1x^2))) sqrt(2)*asin((10*x+1)/(2*sqrt(7)*(x+1))) +sqrt(2)*asin((6*x5)/(2*sqrt(7)*(x1))) +asin((4*x1)/sqrt(7)))/2^(3/2)$ Test of sol: (%i3) f:acos((x1/2)/sqrt(1x^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((1k^2/4)*(1u^2))),u)$ (%i13) subst([k=2/sqrt(5),c=1/2/sqrt(5)],S1),factor; (%o13) integrate(acos((2*u1)/(2*sqrt(1u^2))),u)  >Comment By: Aleksas (aleksasd) Date: 20110907 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 
From: SourceForge.net <noreply@so...>  20110907 09:31:25

Bugs item #3405408, was opened at 20110907 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((x1/2)/sqrt(1x^2)),x); (%o1) (%pi*x)/2 The result should be (%i2) sol:(2^(3/2)*x*acos((2*x1)/(2*sqrt(1x^2))) sqrt(2)*asin((10*x+1)/(2*sqrt(7)*(x+1))) +sqrt(2)*asin((6*x5)/(2*sqrt(7)*(x1))) +asin((4*x1)/sqrt(7)))/2^(3/2)$ Test of sol: (%i3) f:acos((x1/2)/sqrt(1x^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((1k^2/4)*(1u^2))),u)$ (%i13) subst([k=2/sqrt(5),c=1/2/sqrt(5)],S1),factor; (%o13) integrate(acos((2*u1)/(2*sqrt(1u^2))),u)  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3405408&group_id=4933 