[Axiom-developer] mapleok results

[Waldek Hebisch]

Here are results of my analysis of several integrals from mapleok
before and after applying arc tangent patch.  

I had examined a few other integral, but did not record my conclusion.
In general for integrals missing from (rather short) list below I 
make no statement.  To conclude that we get an integral wrong I
was typically satisfied with results of numerical integration. To
conclude that we got integral OK I looked if jump discontinuities are
present (absence of jump discontinuities means we got the integral
correct).  I did some sanity checking for other problems, but
besically I trusted that up to jump discontinuities we get them
correct.

integrate(z/(2-cos(z^2))^2, z=0..2, "noPole")
was wrong
is wrong

in1012a:=integrate(log(abs(z^3-1))/(1+z)^2, z= 0..%plusInfinity,"noPole")
wrong

in1084a:=integrate(atan(sin(z))+atan(1/sin(z)), z= 0..1,"noPole")
wrong

in1118:=integrate(acot(z), z= 0..1/2*I)
was wrong
is OK

in1149:=integrate(imag(z)*z^(1/6), z= -%i..%i)
wrong

in1167a:=integrate((z^2)^(1/6), z= -3..-1,"noPole")
wrong

in1183a:=integrate(csc(z), z= 1-I..1+I,"noPole")
too complicated

in1186a:=integrate((z^2+z)^(1/2)/(1+z^2)^2, z= 0..1,"noPole")
was OK
is wrong

in1190a:=integrate(sin(z)^2*tan(z)^(1/2), z=0..1, "noPole")
was wrong
is wrong
too complicated answer

in1191a:=integrate(sin(z)^2/tan(z)^(1/2), z= 0..1,"noPole")
was wrong
is wrong

in1207a:=integrate(sin(z)*cos(z)*tan(z)^(1/2), z= 0..1, "noPole")
was wrong
is OK

in1214a:=integrate(-sin(z)*tan(z)*csc(z-1), z= 0..1, "noPole")
wrong (is divergent)

in1217a:=integrate(sin(z)*sec(z)*tan(z)^(1/2), z= 0..1,"noPole")
was wrong
is OK

in1218a:=integrate(sin(z)*sec(z)/tan(z)^(1/2), z= 0..1,"noPole")
was wrong
is OK

in15ab:=integrate(log(sqrt(z)+z^5), z=0..a,"noPole")
was wrong
is OK

in1228a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole")
was wrong
is OK

in1248a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole")
duplicate

in1261a:=integrate(1/(sin(z)+cos(2*z)), z= -1..1,"noPole")
wrong (divergent)

in1376a:=integrate(z*acoth(z^(1/2)), z= 0..1,"noPole")
ignored imaginary part

in143a:=integrate(sqrt(1+z)/(1+z^2), z= 0..1,"noPole")
was wrong
is OK

in1933a:=integrate(atan(z)/z/(z*(1+z))^(1/2), z= 0..1,"noPole")
was wrong
is OK

in202a:=integrate(acsc(z), z= 0..1/2,"noPole")
ignored imaginary part
real part was wrong

in2053a:=integrate(atan(2*z-1), z= 0..infinity,"noPole")
was wrong
is OK

integrate(atan(2*z-1), z= 0..%plusInfinity,"noPole")
was wrong
is OK

in2201a:=integrate(acoth(z)+%pi-asec(z-1), z= 0..1,"noPole")
ignored imaginary part
????

in249a:=integrate((sin(z)/(cos(z)-1))^(1/3), z= 0..%pi,"noPole")
ignored imaginary part
????

-- 
                              Waldek Hebisch
address@hidden