On Fri, Jul 08, 2022 at 12:29:31AM +0000, Waldek Hebisch wrote:
> On Thu, Jun 23, 2022 at 09:00:40PM -0700, 'Nasser M. Abbasi' via FriCAS -
> computer algebra system wrote:
> > Thanks for version 1.3.8.
> >
> > I've only did partial test (less than 50%) but regression report generated
> > so far shows there are some integrals no longer evaluate in 1.3.8 but did
> > in 1.3.7. This could be due to bug fix. But thought to let you know just in
> > case.
> <snip>
> > example 5
> > ========
> > using 1.3.7
> > integrate(sec(d*x+c)*(a+b*sin(d*x+c))^(5/2),x)
> > gives this long output
> >
> > [((3*b^2+(-6)*a*b+3*a^2)*((-1)*b+a)^(1/2)*log(((((-8)*b^3*cos(d*x+c)^2+(64*b
> >
> > ^3+(-224)*a*b^2+192*a^2*b))*sin(d*x+c)+((56*b^3+(-80)*a*b^2)*cos(d*x+c)^2+((-
> >
> > 64)*b^3+160*a*b^2+(-192)*a^2*b+128*a^3)))*((-1)*b+a)^(1/2)*(b*sin(d*x+c)+a)^(
> >
> > 1/2)+((((-28)*b^4+32*a*b^3)*cos(d*x+c)^2+(56*b^4+(-256)*a*b^3+448*a^2*b^2+(-2
> >
> > 56)*a^3*b))*sin(d*x+c)+((-1)*b^4*cos(d*x+c)^4+(72*b^4+(-224)*a*b^3+160*a^2*b^
> >
> > 2)*cos(d*x+c)^2+((-72)*b^4+256*a*b^3+(-320)*a^2*b^2+256*a^3*b+(-128)*a^4))))/
> >
> > ((4*cos(d*x+c)^2+(-8))*sin(d*x+c)+((-1)*cos(d*x+c)^4+8*cos(d*x+c)^2+(-8))))+(
> >
> > (3*b^2+6*a*b+3*a^2)*(b+a)^(1/2)*log(((((-8)*b^3*cos(d*x+c)^2+(64*b^3+224*a*b^
> >
> > 2+192*a^2*b))*sin(d*x+c)+(((-56)*b^3+(-80)*a*b^2)*cos(d*x+c)^2+(64*b^3+160*a*
> >
> > b^2+192*a^2*b+128*a^3)))*(b+a)^(1/2)*(b*sin(d*x+c)+a)^(1/2)+((((-28)*b^4+(-32
> >
> > )*a*b^3)*cos(d*x+c)^2+(56*b^4+256*a*b^3+448*a^2*b^2+256*a^3*b))*sin(d*x+c)+(b
> >
> > ^4*cos(d*x+c)^4+((-72)*b^4+(-224)*a*b^3+(-160)*a^2*b^2)*cos(d*x+c)^2+(72*b^4+
> >
> > 256*a*b^3+320*a^2*b^2+256*a^3*b+128*a^4))))/((4*cos(d*x+c)^2+(-8))*sin(d*x+c)
> >
> > +(cos(d*x+c)^4+(-8)*cos(d*x+c)^2+8)))+((-16)*b^2*sin(d*x+c)+(-112)*a*b)*(b*si
> >
> > n(d*x+c)+a)^(1/2)))/(24*d),((3*b^2+(-6)*a*b+3*a^2)*((-1)*b+a)^(1/2)*log(((((-
> >
> > 8)*b^3*cos(d*x+c)^2+(64*b^3+(-224)*a*b^2+192*a^2*b))*sin(d*x+c)+((56*b^3+(-80
> >
> > )*a*b^2)*cos(d*x+c)^2+((-64)*b^3+160*a*b^2+(-192)*a^2*b+128*a^3)))*((-1)*b+a)
> >
> > ^(1/2)*(b*sin(d*x+c)+a)^(1/2)+((((-28)*b^4+32*a*b^3)*cos(d*x+c)^2+(56*b^4+(-2
> >
> > 56)*a*b^3+448*a^2*b^2+(-256)*a^3*b))*sin(d*x+c)+((-1)*b^4*cos(d*x+c)^4+(72*b^
> >
> > 4+(-224)*a*b^3+160*a^2*b^2)*cos(d*x+c)^2+((-72)*b^4+256*a*b^3+(-320)*a^2*b^2+
> >
> > 256*a^3*b+(-128)*a^4))))/((4*cos(d*x+c)^2+(-8))*sin(d*x+c)+((-1)*cos(d*x+c)^4
> >
> > +8*cos(d*x+c)^2+(-8))))+(((-6)*b^2+(-12)*a*b+(-6)*a^2)*((-1)*b+(-1)*a)^(1/2)*
> >
> > atan((((6*b^2+8*a*b)*sin(d*x+c)+((-1)*b^2*cos(d*x+c)^2+(2*b^2+8*a*b+8*a^2)))*
> >
> > ((-1)*b+(-1)*a)^(1/2)*(b*sin(d*x+c)+a)^(1/2))/((4*b^3+16*a*b^2+12*a^2*b)*sin(
> >
> > d*x+c)+(((-4)*b^3+(-4)*a*b^2)*cos(d*x+c)^2+(4*b^3+8*a*b^2+12*a^2*b+8*a^3))))+
> >
> > ((-16)*b^2*sin(d*x+c)+(-112)*a*b)*(b*sin(d*x+c)+a)^(1/2)))/(24*d),((3*b^2+6*a
> >
> > *b+3*a^2)*(b+a)^(1/2)*log(((((-8)*b^3*cos(d*x+c)^2+(64*b^3+224*a*b^2+192*a^2*
> >
> > b))*sin(d*x+c)+(((-56)*b^3+(-80)*a*b^2)*cos(d*x+c)^2+(64*b^3+160*a*b^2+192*a^
> >
> > 2*b+128*a^3)))*(b+a)^(1/2)*(b*sin(d*x+c)+a)^(1/2)+((((-28)*b^4+(-32)*a*b^3)*c
> >
> > os(d*x+c)^2+(56*b^4+256*a*b^3+448*a^2*b^2+256*a^3*b))*sin(d*x+c)+(b^4*cos(d*x
> >
> > +c)^4+((-72)*b^4+(-224)*a*b^3+(-160)*a^2*b^2)*cos(d*x+c)^2+(72*b^4+256*a*b^3+
> >
> > 320*a^2*b^2+256*a^3*b+128*a^4))))/((4*cos(d*x+c)^2+(-8))*sin(d*x+c)+(cos(d*x+
> >
> > c)^4+(-8)*cos(d*x+c)^2+8)))+(((-6)*b^2+12*a*b+(-6)*a^2)*(b+(-1)*a)^(1/2)*atan
> >
> > ((((6*b^2+(-8)*a*b)*sin(d*x+c)+(b^2*cos(d*x+c)^2+((-2)*b^2+8*a*b+(-8)*a^2)))*
> >
> > (b+(-1)*a)^(1/2)*(b*sin(d*x+c)+a)^(1/2))/((4*b^3+(-16)*a*b^2+12*a^2*b)*sin(d*
> >
> > x+c)+((4*b^3+(-4)*a*b^2)*cos(d*x+c)^2+((-4)*b^3+8*a*b^2+(-12)*a^2*b+8*a^3))))
> >
> > +((-16)*b^2*sin(d*x+c)+(-112)*a*b)*(b*sin(d*x+c)+a)^(1/2)))/(24*d),(((-3)*b^2
> >
> > +6*a*b+(-3)*a^2)*(b+(-1)*a)^(1/2)*atan((((6*b^2+(-8)*a*b)*sin(d*x+c)+(b^2*cos
> >
> > (d*x+c)^2+((-2)*b^2+8*a*b+(-8)*a^2)))*(b+(-1)*a)^(1/2)*(b*sin(d*x+c)+a)^(1/2)
> >
> > )/((4*b^3+(-16)*a*b^2+12*a^2*b)*sin(d*x+c)+((4*b^3+(-4)*a*b^2)*cos(d*x+c)^2+(
> >
> > (-4)*b^3+8*a*b^2+(-12)*a^2*b+8*a^3))))+(((-3)*b^2+(-6)*a*b+(-3)*a^2)*((-1)*b+
> >
> > (-1)*a)^(1/2)*atan((((6*b^2+8*a*b)*sin(d*x+c)+((-1)*b^2*cos(d*x+c)^2+(2*b^2+8
> >
> > *a*b+8*a^2)))*((-1)*b+(-1)*a)^(1/2)*(b*sin(d*x+c)+a)^(1/2))/((4*b^3+16*a*b^2+
> >
> > 12*a^2*b)*sin(d*x+c)+(((-4)*b^3+(-4)*a*b^2)*cos(d*x+c)^2+(4*b^3+8*a*b^2+12*a^
> >
> > 2*b+8*a^3))))+((-8)*b^2*sin(d*x+c)+(-56)*a*b)*(b*sin(d*x+c)+a)^(1/2)))/(12*d)
> > ]
> > But does not evaluate in 1.3.8
>
> Actually, this is really not a regression. This integral works or
> fails randomly both in 1.3.7 and 1.3.8. I will look more deeply
> to see what is happening.
This problem is now fixed in the trunk. This integral probably
in unlucky cases may give division by zero, but it should never
return unevaluated.
--
Waldek Hebisch
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