Problem with change of variables in an integral

• To: mathgroup at smc.vnet.net
• Subject: [mg131569] Problem with change of variables in an integral
• From: "Dr. Robert Kragler" <kragler at hs-weingarten.de>
• Date: Tue, 3 Sep 2013 23:34:53 -0400 (EDT)
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```Hello,

Although I know how to make a change of variables in an integral I can only do
it manually by applying a substitution rule to the integrand and the
differential e.g
{f[z],\[DifferentialD]z}//. {z-> r E^(I
\[Phi]),\[DifferentialD]z->E^(I \[Phi]) \[DifferentialD]r,\[Phi] -> (2\[Pi])/3}

But it cannot applied this substitution rule directly to the integral, e.g.
Integrate[f[z],{z,0,\[Infinity]}] //. {z-> r E^(I
\[Phi]),\[DifferentialD]z->E^(I \[Phi]) \[DifferentialD]r,\[Phi] -> (2\[Pi])/3}

Comparing with the correct result, the exponential factor E^((2 I \[Pi])/3) =
(-1)^(2/3) is missing in the evaluation of the integral. The correct appearance
of the
integral is :  Integrate[1/(1+r^3) E^((2 I \[Pi])/3),{r,0,\[Infinity]}]

How can I force Mathematica (V8) to perform the correct transformation of
variables as regards to the integral (and not to its separate parts of it as
{f[z],\[DifferentialD]z} ?

Any suggestions are appreciated.
Robert Kragler

--
Robert Kragler
Email : kragler at hs-weingarten.de
URL :   http://portal.hs-weingarten.de/web/kragler

```

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