7.89 bug in integration in Maple 6 and Maple 7 (27.11.00)

7.89.1 Halvor Mehlum

I get the following inconsistency on my Windows 98 running Maple 6

As part of my work I executed the following code:

a1 := .9*(.9+8.*exp(-1))*exp(.1*tt)/(1+8*exp(-1)): 
b1:=int(exp(-tt)*ln(a2),tt=t..1): 
c1:=evalf(subs(t=0.5,b1)); 
a2:=simplify(a1): 
b2:=int(exp(-tt)*ln(a1),tt=t..1): 
c2:=evalf(subs(t=0.5,b2)); 
The result was as follows 
 
    c1 := -.01387124925 
    c2 := -.02000179884
 

which is surprising as they are supposed to be identical. The expressions b1 and b2 are also different. Does the same problem arise on other machines?

It is corrected with Maple 8 (U. Klein)

7.89.2 Don Hartig (27.11.00)

I assume that the a2 appearing in the expression for b1 should actually be a1. If that is the case, then I get the same values for c1 and c2. I also get the same values for b1 and b2.

I am running Maple 6.1 on a Macintosh G4.

7.89.3 Robert Israel (28.11.00)

Yes, it’s a bug. It shows up in a simpler form here:

> f:= exp(-t)*ln(exp(t/2)/(1+exp(1))); 
  int(f,t); 
 
                    2                 2 
  - 1/2 exp(- 1/2 t)  + 2 exp(- 1/2 t)  ln(1 + exp(1)) 
 
                             2 
         - 1/2 t exp(- 1/2 t)
 

The 2 in front of the second term should be 1. The bug seems to be new in Maple 6: it doesn’t affect Maple V Releases 4 to 5.1.

This is corrected with Maple 7. (U. Klein)

7.89.4 Heike Koch-Beuttenmueller (28.11.00)

Things seems to be even much stranger:

I tried the following on Compac Alpha:

d1 := 9/10*(9/10+8*exp(-1))*exp(1/10*tt)/(1+8*exp(-1)); 
 
int(exp(-tt)*log(d1),tt=1/2..1); 
 
-1/5*exp(-1)-2*exp(-1)*ln(3)+3*exp(-1)*ln(2)+3*exp(-1)*ln(5)-2*exp(-1) 
*ln(9+80*exp(-1))+2*exp(-1)*ln(1+8*exp(-1))+3/20*exp(-1/2)+2*exp(-1/2) 
*ln(3)-3*exp(-1/2)*ln(2)-3*exp(-1/2)*ln(5)+2*exp(-1/2)*ln(9+80*exp(-1) 
 
evalf(%,30); 
                   -.02000179714067499958474512972 
 
int(exp(-tt)*log(d1),tt=0.5..1); 
 
                            -.01387125093
 

Mathematica gives the last result. Numerical integration with Maple as well.