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multivariate integral

Hi experts!

For obtain the pdf of a multivariate function of random variables i must resolve explicitly a multivariate integral and then derivate it:

http://math.stackexchange.com/questions/624958/how-to-obtain-a-pdf-of-a-random-variable-defined-as-a-function-of-many-variables/

How can I resolve my problem in SAGE?

Waiting for yor answers.

Thanks a lot!!