> integral(sqrt(1+cos(x)^2),x,0,pi) > > > > 0 > > The bug appears to be tickled by the Maxima package abs_integrate. > Without abs_integrate, integrate(sqrt(1 + cos(x)^2), x, 0, %pi) just > returns a noun expression. > > > Zero is decidedly not correct. The problem is apparently here: > > > > integral(sqrt(1+cos(x)^2),x) > > > > -1/24*sin(3*x) + 1/8*sin(x) > > Hmm, for the indefinite integral I get (with abs_integrate) > > (%i4) integrate(sqrt(1+cos(x)^2),x); > (%o4) ((2*sin(3*x)+6*sin(x))*false-sin(3*x)+3*sin(x))/24 > > See https://trac.sagemath.org/ticket/12731 for lots more examples (also https://trac.sagemath.org/wiki/symbolics#Integrationtickets). A lot of these are reported upstream but since we are using the package I think they are less likely to get attention than core Maxima functionality. (And I haven't been helpful lately on them either, so no aspersions are being cast.)
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