From: SourceForge.net <noreply@so...>  20090830 21:27:34

Bugs item #2847436, was opened at 20090830 21:27 Message generated for change (Tracker Item Submitted) made by nobody You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847436&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: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(sqrt(t)*log(t)^(1/2),t,0,1) wrong sign Initial Comment: The following two integrals have the wrong sign: integrate(sqrt(t)*log(t)^(1/2),t,0,1) and integrate(sqrt(t)*log(t)^(1/2),t,0,1) It is interesting that Maxima is able to solve the more general type: (%i164) declare(s,noninteger); (%o164) done (%i165) expr:integrate(sqrt(t)*log(t)^s,t,0,1); (%o165) 3^(s1)*(1)^s*2^(s+1)*gamma_incomplete(s+1,0) For s=1/2 and s=1/2 we get the answers: (%i167) expr,s=1/2; (%o167) sqrt(2)*sqrt(%pi)*%i/(2*sqrt(3)) (%i168) expr,s=1/2; (%o168) sqrt(2)*sqrt(%pi)*%i/sqrt(3) Both solutions can be checked to be correct. Now we do it directly: (%i4) integrate(sqrt(t)*log(t)^(1/2),t,0,1); (%o4) %i*('limit(sqrt(2)*sqrt(%pi)*erf(sqrt(3)*sqrt(log(t))/sqrt(2))/3^(3/2) 2*t^(3/2)*sqrt(log(t))/3,t,0,plus)) We need an extra evaluation, but this is another problem: (%i5) %,nouns; (%o5) sqrt(2)*sqrt(%pi)*%i/3^(3/2) Now the integral for s=1/2: (%i6) integrate(sqrt(t)*log(t)^(1/2),t,0,1); (%o6) sqrt(2)*sqrt(%pi)*%i/sqrt(3) These solutions differ by the sign with the answers from above. I have checked it for a lot of other values for the parameter s. In all other cases the result of the integral and the more general solution are equal. Remark: The integral is divergent for s a negative integer. For these cases the gamma_incomplete function is not defined. Dieter Kaiser  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847436&group_id=4933 