## [Maxima-bugs] [ maxima-Bugs-3529696 ] Problems with integral (x/(exp(x)+1), x, 0, inf)

 [Maxima-bugs] [ maxima-Bugs-3529696 ] Problems with integral (x/(exp(x)+1), x, 0, inf) From: SourceForge.net - 2012-05-25 08:13:28 ```Bugs item #3529696, was opened at 2012-05-25 01:13 Message generated for change (Tracker Item Submitted) made by chrisrein You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3529696&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: christoph reineke (chrisrein) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with integral (x/(exp(x)+1),x,0,inf) Initial Comment: The correct result of integrate(x/(exp(x)+1),x,0,inf); should be pi^2/12. Maxima returns: (%o2) limit(-x*log(%e^x+1)-li[2](-%e^x)+x^2/2,x,inf,minus)-%pi^2/12 build_info("5.27.0","2012-04-24 08:52:03","i686-pc-mingw32","GNU Common Lisp (GCL)","GCL 2.6.8") regards chris ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3529696&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-3529696 ] Problems with integral (x/(exp(x)+1), x, 0, inf) From: SourceForge.net - 2012-05-25 08:13:28 ```Bugs item #3529696, was opened at 2012-05-25 01:13 Message generated for change (Tracker Item Submitted) made by chrisrein You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3529696&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: christoph reineke (chrisrein) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with integral (x/(exp(x)+1),x,0,inf) Initial Comment: The correct result of integrate(x/(exp(x)+1),x,0,inf); should be pi^2/12. Maxima returns: (%o2) limit(-x*log(%e^x+1)-li[2](-%e^x)+x^2/2,x,inf,minus)-%pi^2/12 build_info("5.27.0","2012-04-24 08:52:03","i686-pc-mingw32","GNU Common Lisp (GCL)","GCL 2.6.8") regards chris ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3529696&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3529696 ] Problems with integral (x/(exp(x)+1), x, 0, inf) From: SourceForge.net - 2012-05-29 08:13:32 ```Bugs item #3529696, was opened at 2012-05-25 01:13 Message generated for change (Comment added) made by aleksasd You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3529696&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: christoph reineke (chrisrein) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with integral (x/(exp(x)+1),x,0,inf) Initial Comment: The correct result of integrate(x/(exp(x)+1),x,0,inf); should be pi^2/12. Maxima returns: (%o2) limit(-x*log(%e^x+1)-li[2](-%e^x)+x^2/2,x,inf,minus)-%pi^2/12 build_info("5.27.0","2012-04-24 08:52:03","i686-pc-mingw32","GNU Common Lisp (GCL)","GCL 2.6.8") regards chris ---------------------------------------------------------------------- Comment By: Aleksas (aleksasd) Date: 2012-05-29 01:13 Message: my solution: (%i1) S:'integrate(x/(exp(x)+1),x,0,inf)\$ (%i2) intparts(S,u):=block([f,var,v,a,b], f:part(S,1),var:part(S,2),v:integrate(f/u,var), if last(S)#var then (a:part(S,3),b:part(S,4), limit(u*v,var,b,minus)-limit(u*v,var,a,plus) -'integrate(v*diff(u,var),var,a,b)) else u*v-'integrate(v*diff(u,var),var) )\$ (%i3) intparts(S,1/(exp(x)+1)); (%o3) integrate((x^2*%e^x)/(%e^x+1)^2,x,0,inf)/2 (%i4) ev(%, nouns); (%o4) %pi^2/12 (%i5) float(%), numer; (%o5) 0.82246703342411 (%i6) quad_qagi(x/(%e^x+1), x, 0, inf); (%o6) [0.82246703342411,5.9689712369638092*10^-10,135,0] Aleksas D ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3529696&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3529696 ] Problems with integral (x/(exp(x)+1), x, 0, inf) From: SourceForge.net - 2012-05-29 12:27:34 ```Bugs item #3529696, was opened at 2012-05-25 01:13 Message generated for change (Comment added) made by chrisrein You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3529696&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: christoph reineke (chrisrein) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with integral (x/(exp(x)+1),x,0,inf) Initial Comment: The correct result of integrate(x/(exp(x)+1),x,0,inf); should be pi^2/12. Maxima returns: (%o2) limit(-x*log(%e^x+1)-li[2](-%e^x)+x^2/2,x,inf,minus)-%pi^2/12 build_info("5.27.0","2012-04-24 08:52:03","i686-pc-mingw32","GNU Common Lisp (GCL)","GCL 2.6.8") regards chris ---------------------------------------------------------------------- >Comment By: christoph reineke (chrisrein) Date: 2012-05-29 05:27 Message: Thank you very much! By the way, we have the same problem with the similar expression integrate(x/(exp(x)-1),x,0,inf)=pi^2/6. Sorry, I noticed that after submitting my first message! Regards Chris ---------------------------------------------------------------------- Comment By: Aleksas (aleksasd) Date: 2012-05-29 01:13 Message: my solution: (%i1) S:'integrate(x/(exp(x)+1),x,0,inf)\$ (%i2) intparts(S,u):=block([f,var,v,a,b], f:part(S,1),var:part(S,2),v:integrate(f/u,var), if last(S)#var then (a:part(S,3),b:part(S,4), limit(u*v,var,b,minus)-limit(u*v,var,a,plus) -'integrate(v*diff(u,var),var,a,b)) else u*v-'integrate(v*diff(u,var),var) )\$ (%i3) intparts(S,1/(exp(x)+1)); (%o3) integrate((x^2*%e^x)/(%e^x+1)^2,x,0,inf)/2 (%i4) ev(%, nouns); (%o4) %pi^2/12 (%i5) float(%), numer; (%o5) 0.82246703342411 (%i6) quad_qagi(x/(%e^x+1), x, 0, inf); (%o6) [0.82246703342411,5.9689712369638092*10^-10,135,0] Aleksas D ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3529696&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3529696 ] Problems with integral (x/(exp(x)+1), x, 0, inf) From: SourceForge.net - 2012-05-29 20:16:24 ```Bugs item #3529696, was opened at 2012-05-25 01:13 Message generated for change (Comment added) made by aleksasd You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3529696&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: christoph reineke (chrisrein) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with integral (x/(exp(x)+1),x,0,inf) Initial Comment: The correct result of integrate(x/(exp(x)+1),x,0,inf); should be pi^2/12. Maxima returns: (%o2) limit(-x*log(%e^x+1)-li[2](-%e^x)+x^2/2,x,inf,minus)-%pi^2/12 build_info("5.27.0","2012-04-24 08:52:03","i686-pc-mingw32","GNU Common Lisp (GCL)","GCL 2.6.8") regards chris ---------------------------------------------------------------------- Comment By: Aleksas (aleksasd) Date: 2012-05-29 13:16 Message: Solution of the second problem: (%i1) S:'integrate(x/(exp(x)-1),x,0,inf); (%o1) integrate(x/(%e^x-1),x,0,inf) (%i2) intparts(S,u):=block([f,var,v,a,b], f:part(S,1),var:part(S,2),v:integrate(f/u,var), if last(S)#var then (a:part(S,3),b:part(S,4), limit(u*v,var,b,minus)-limit(u*v,var,a,plus) -'integrate(v*diff(u,var),var,a,b)) else u*v-'integrate(v*diff(u,var),var) )\$ (%i3) changevar(S, y=exp(x)-1, y, x); (%o3) integrate(log(y+1)/(y^2+y),y,0,inf) (%i4) intparts(%,log(y+1)); (%o4) -integrate((log(y)-log(y+1))/(y+1),y,0,inf) (%i5) logcontract(%); (%o5) -integrate(log(y/(y+1))/(y+1),y,0,inf) (%i6) ev(%, nouns); (%o6) %pi^2/6 Aleksas D ---------------------------------------------------------------------- Comment By: christoph reineke (chrisrein) Date: 2012-05-29 05:27 Message: Thank you very much! By the way, we have the same problem with the similar expression integrate(x/(exp(x)-1),x,0,inf)=pi^2/6. Sorry, I noticed that after submitting my first message! Regards Chris ---------------------------------------------------------------------- Comment By: Aleksas (aleksasd) Date: 2012-05-29 01:13 Message: my solution: (%i1) S:'integrate(x/(exp(x)+1),x,0,inf)\$ (%i2) intparts(S,u):=block([f,var,v,a,b], f:part(S,1),var:part(S,2),v:integrate(f/u,var), if last(S)#var then (a:part(S,3),b:part(S,4), limit(u*v,var,b,minus)-limit(u*v,var,a,plus) -'integrate(v*diff(u,var),var,a,b)) else u*v-'integrate(v*diff(u,var),var) )\$ (%i3) intparts(S,1/(exp(x)+1)); (%o3) integrate((x^2*%e^x)/(%e^x+1)^2,x,0,inf)/2 (%i4) ev(%, nouns); (%o4) %pi^2/12 (%i5) float(%), numer; (%o5) 0.82246703342411 (%i6) quad_qagi(x/(%e^x+1), x, 0, inf); (%o6) [0.82246703342411,5.9689712369638092*10^-10,135,0] Aleksas D ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3529696&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3529696 ] Problems with integral (x/(exp(x)+1), x, 0, inf) From: SourceForge.net - 2012-05-30 11:23:57 ```Bugs item #3529696, was opened at 2012-05-25 01:13 Message generated for change (Comment added) made by chrisrein You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3529696&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: christoph reineke (chrisrein) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with integral (x/(exp(x)+1),x,0,inf) Initial Comment: The correct result of integrate(x/(exp(x)+1),x,0,inf); should be pi^2/12. Maxima returns: (%o2) limit(-x*log(%e^x+1)-li[2](-%e^x)+x^2/2,x,inf,minus)-%pi^2/12 build_info("5.27.0","2012-04-24 08:52:03","i686-pc-mingw32","GNU Common Lisp (GCL)","GCL 2.6.8") regards chris ---------------------------------------------------------------------- >Comment By: christoph reineke (chrisrein) Date: 2012-05-30 04:23 Message: Yes, it works. Thanks again! Shall we close this bug report? Regards Chris ---------------------------------------------------------------------- Comment By: Aleksas (aleksasd) Date: 2012-05-29 13:16 Message: Solution of the second problem: (%i1) S:'integrate(x/(exp(x)-1),x,0,inf); (%o1) integrate(x/(%e^x-1),x,0,inf) (%i2) intparts(S,u):=block([f,var,v,a,b], f:part(S,1),var:part(S,2),v:integrate(f/u,var), if last(S)#var then (a:part(S,3),b:part(S,4), limit(u*v,var,b,minus)-limit(u*v,var,a,plus) -'integrate(v*diff(u,var),var,a,b)) else u*v-'integrate(v*diff(u,var),var) )\$ (%i3) changevar(S, y=exp(x)-1, y, x); (%o3) integrate(log(y+1)/(y^2+y),y,0,inf) (%i4) intparts(%,log(y+1)); (%o4) -integrate((log(y)-log(y+1))/(y+1),y,0,inf) (%i5) logcontract(%); (%o5) -integrate(log(y/(y+1))/(y+1),y,0,inf) (%i6) ev(%, nouns); (%o6) %pi^2/6 Aleksas D ---------------------------------------------------------------------- Comment By: christoph reineke (chrisrein) Date: 2012-05-29 05:27 Message: Thank you very much! By the way, we have the same problem with the similar expression integrate(x/(exp(x)-1),x,0,inf)=pi^2/6. Sorry, I noticed that after submitting my first message! Regards Chris ---------------------------------------------------------------------- Comment By: Aleksas (aleksasd) Date: 2012-05-29 01:13 Message: my solution: (%i1) S:'integrate(x/(exp(x)+1),x,0,inf)\$ (%i2) intparts(S,u):=block([f,var,v,a,b], f:part(S,1),var:part(S,2),v:integrate(f/u,var), if last(S)#var then (a:part(S,3),b:part(S,4), limit(u*v,var,b,minus)-limit(u*v,var,a,plus) -'integrate(v*diff(u,var),var,a,b)) else u*v-'integrate(v*diff(u,var),var) )\$ (%i3) intparts(S,1/(exp(x)+1)); (%o3) integrate((x^2*%e^x)/(%e^x+1)^2,x,0,inf)/2 (%i4) ev(%, nouns); (%o4) %pi^2/12 (%i5) float(%), numer; (%o5) 0.82246703342411 (%i6) quad_qagi(x/(%e^x+1), x, 0, inf); (%o6) [0.82246703342411,5.9689712369638092*10^-10,135,0] Aleksas D ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3529696&group_id=4933 ```