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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*Reply-to*: kragler at hs-weingarten.de

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

**Follow-Ups**:**Re: Problem with change of variables in an integral***From:*Murray Eisenberg <murrayeisenberg@gmail.com>