bug (?) in Integrate (5.2)

• To: mathgroup at smc.vnet.net
• Subject: [mg76113] bug (?) in Integrate (5.2)
• From: dimitris <dimmechan at yahoo.com>
• Date: Wed, 16 May 2007 05:38:07 -0400 (EDT)

```Hello.

In[51]:=
int1 = (1/(2*Pi*I))*Integrate[1/o, {o, 1, I, -1, -I, 1}]   (*correct*)
Out[51]=
1

In[52]:=
int2 = (1/(2*Pi*I))*Integrate[1/o, {o, r, r*I, -r, (-r)*I, r},
Assumptions -> r > 0]  (*correct*)
Out[52]=
1

In[53]:=
int3 = (1/(2*Pi*I))*Integrate[Exp[2/o], {o, 1, I, -1, -I, 1}]
(*correct*)
Out[53]=
2

In[54]:=
int4 = Simplify[(1/(2*Pi*I))*Integrate[Exp[2/o], {o, r, r*I, -r, (-
r)*I, r}, Assumptions -> r > 0]]  (*incorrect*)
Out[54]=
0

It should be 2.

In[70]:=
Exp[2/z]*dz /. z -> Exp[I*u] /. dz -> D[Exp[I*u], u]
(1/(2*Pi*I))*Integrate[%, {u, 0, 2*Pi}]  (*correct*)

Out[70]=
I*E^(2/E^(I*u) + I*u)
Out[71]=
2

In[72]:=
Exp[2/z]*dz /. z -> R*Exp[I*u] /. dz -> D[R*Exp[I*u], u]
(1/(2*Pi*I))*Integrate[%, {u, 0, 2*Pi}] (*incorrect*)

Out[72]=
I*E^(2/(E^(I*u)*R) + I*u)*R

Out[73]=
0

It should be zero.

Any comments?
What does version 6 do?

Dimitris

```

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