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From: SourceForge.net <noreply@so...>  20120622 16:47:20

Bugs item #3536939, was opened at 20120621 09:04 Message generated for change (Comment added) made by aleksasd You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3536939&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: No result for definite integral (II) Initial Comment: Enter in Maxima: integrate(sin(x)/x*log(x),x,0,inf) and Maxima returns: integrate((log(x)*sin(x))/x,x,0,inf) The correct result is: (%pi*gamma)/2, gamma=Euler's constant. build_info("5.27.0","20120424 08:52:03","i686pcmingw32","GNU Common Lisp (GCL)","GCL 2.6.8") Regards Chris  Comment By: Aleksas (aleksasd) Date: 20120622 09:47 Message: Problem: integrate(sin(x)*log(x)/x,x,0,inf) We use laplace integral transformations metrhod. (%i1) declare(integrate,linear)$ (%i2) assume(s>0)$ (%i3) S:'integrate(sin(x)*log(x*a)/x,x,0,inf)$ (%i4) f:first(S); (%o4) (sin(x)*log(a*x))/x (%i5) laplace(%,a,s); (%o5) ((log(x)log(s)%gamma)*sin(x))/(s*x) (%i6) integrate(%,x,0,inf),expand; (%o6) integrate((log(x)*sin(x))/x,x,0,inf)/s(log(s)*integrate(sin(x)/x,x,0,inf))/s(%gamma*integrate(sin(x)/x,x,0,inf))/s (%i7) ev(%, nouns); (%o7) integrate((log(x)*sin(x))/x,x,0,inf)/s(%pi*log(s))/(2*s)(%gamma*%pi)/(2*s) (%i8) eq1:S=ilt(%,s,a); (%o8) integrate((sin(x)*log(a*x))/x,x,0,inf)=integrate((log(x)*sin(x))/x,x,0,inf)+ilt((%pi*log(s))/(2*s),s,a)+(%gamma*%pi)/2 (%i9) S1:'integrate(sin(a*x)*log(x)/x,x,0,inf)$ (%i10) f:first(S1); (%o10) (log(x)*sin(a*x))/x (%i11) laplace(%,a,s); (%o11) log(x)/(x^2+s^2) (%i12) integrate(%,x,0,inf); (%o12) (%pi*log(s))/(2*s) (%i13) eq2:S1=ilt(%,s,a); (%o13) integrate((log(x)*sin(a*x))/x,x,0,inf)=ilt((%pi*log(s))/(2*s),s,a) (%i14) subst(a=1,[eq1,eq2]); (%o14) [integrate((log(x)*sin(x))/x,x,0,inf)=integrate((log(x)*sin(x))/x,x,0,inf)+ilt((%pi*log(s))/(2*s),s,1)+(%gamma*%pi)/2,integrate((log(x)*sin(x))/x,x,0,inf)=ilt((%pi*log(s))/(2*s),s,1)] (%i15) solve(%,[integrate((log(x)*sin(x))/x,x,0,inf),ilt((%pi*log(s))/(2*s),s,1)]); (%o15) [[integrate((log(x)*sin(x))/x,x,0,inf)=(%gamma*%pi)/2,ilt((%pi*log(s))/(2*s),s,1)=(%gamma*%pi)/2]] (%i16) solution:%[1][1]; (%o16) integrate((log(x)*sin(x))/x,x,0,inf)=(%gamma*%pi)/2 Best Aleksas D  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3536939&group_id=4933 