One of Moses's examples is:
(%i1) f:sqrt(a^2+b^2*sin(x)^2)/sin(x); 2 2 2 sqrt(b sin (x) + a ) (%o1) --------------------- sin(x) (%i2) g:integrate(f,x); Is a zero or nonzero? nonzero; 4 2 2 Is b + a b positive or zero? positive; Is b zero or nonzero? nonzero; 2 2 2 2 2 2 abs(a) sqrt((- b cos (x)) + b + a ) 2 a 2 abs(a) log(--------------------------------------- + ------------ - b ) 2 cos(x) + 2 2 cos(x) + 2 (%o2) ----------------------------------------------------------------------- 2 2 2 2 2 2 2 abs(a) sqrt((- b cos (x)) + b + a ) 2 a 2 abs(a) log(--------------------------------------- + ------------ + b ) 2 - 2 cos(x) 2 - 2 cos(x) - ----------------------------------------------------------------------- 2 2 b cos(x) - abs(b) asin(----------------) 4 2 2 sqrt(b + a b ) (%i3) diff(g,x)-f; 2 2 2 sqrt(b sin (x) + a ) (%o3) (- ---------------------) + (abs(a) sin(x) 2 2 2 2 4 abs(a) sqrt((- b cos (x)) + b + a ) sin(x) (---------------------------------------------- 2 (2 cos(x) + 2) 2 2 2 abs(a) b cos(x) sin(x) 4 a sin(x) + --------------------------------------------- + ---------------)) 2 2 2 2 2 (2 cos(x) + 2) sqrt((- b cos (x)) + b + a ) (2 cos(x) + 2) 2 2 2 2 2 2 abs(a) sqrt((- b cos (x)) + b + a ) 2 a 2 /(2 (--------------------------------------- + ------------ - b )) 2 cos(x) + 2 2 cos(x) + 2 2 2 2 2 4 abs(a) sqrt((- b cos (x)) + b + a ) sin(x) - (abs(a) ((- ----------------------------------------------) 2 (2 - 2 cos(x)) 2 2 2 abs(a) b cos(x) sin(x) 4 a sin(x) + --------------------------------------------- - ---------------)) 2 2 2 2 2 (2 - 2 cos(x)) sqrt((- b cos (x)) + b + a ) (2 - 2 cos(x)) 2 2 2 2 2 2 abs(a) sqrt((- b cos (x)) + b + a ) 2 a 2 /(2 (--------------------------------------- + ------------ + b )) 2 - 2 cos(x) 2 - 2 cos(x) 2 b abs(b) sin(x) + ------------------------------------- 4 2 4 2 2 b cos (x) sqrt(b + a b ) sqrt(1 - ----------) 4 2 2 b + a b (%i4) %,a=1.3,b=0.4,x=2.3; (%o4) 0.04485309515590674
Maxima 5.41.0 using Lisp GNU Common Lisp (GCL) GCL 2.6.12 on Ubuntu 18.04.
I get this for the integral when using Macsyma 2.4. This does give zero when diff(g,x)-f is executed and simplified.
If I am not mistaken, the difference is the sign of the b^2 term in the first log(). If I change that, and evaluate the derivative minus the original function at some random points numerically, I get indeed zero.
Also, it evaluates to zero now, if I use factor, then exponentialize, and then radcan.
Last edit: arpi 2019-03-25
Diff:
I have checked, and the bug is still present in 5.43.2.