# Question:Maple having difficulty with straight-forward integral

## Question:Maple having difficulty with straight-forward integral

Maple

Hi There,

Here's the problem: I'm trying to tiple-integrate rst e with the limits...
t=r-s...r+s
s=r...∞
r=0...∞

This is a straighforward integral with the use of the gamma function

0 xe dr = Γ(n+1)/a

and my copy of Maple v11 crashes before it yields the answer.

However, when I try evaluating the slightly simpler integral rst e with the same limits

t=r-s...r+s
s=r...∞
r=0...∞

It yields the answer in under 10 seconds.  I am guessing Maple has a problem with the first integral because the answer will have things like (β+λ) in the denominator which it will try and expand out.  Is there a way to prevent Maple from expanding these expressions when it does the integral?

My plan to remedy this problem is to write a maple function with the proc() command that takes the integral and applies the gamma function rule to it.  My only problem is that I don't know the maple command that can take the function as its input (ie. rst e )and gives the exponent on the r as its output.  For example: Yield_Exponent(rst e,r); when typed into maple would give the answer 4.

So my questions are:
1. Is there a way to help Maple solve this integral more quickly? (perhaps a way to prevent maple from expanding the expressions in the denominator)
2. Is there a maple function (like Yield_Exponent(rst e,r);) that can take a mathematical function as input and give the exponent on one of the variables as it's output?

Thank you for the help everyone, and thanks to those who took the time to read my problem!

-Mike Busuttil

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