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Substiuting variables within an integral


I need to do a variable substitution within an integral in several different
ways. I need Mathematica to rearrange the integral with the new variable
definition without solving it.   The resulting integral will be variations
of Euler function.  After seeing the resulting integral, I need Mathematica
to actually solve it for me (that is, Mathematica needs to recognize that it
is an Euler function).  Can this be done?

Many thanks


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