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well here's my problem: I got this integral and I don't know how to calculate it (I am trying to find if there exists a k that satisfies this relation) :

[tex] \int_0^k \frac{1}{ ( 4k-4r-2 ) ! ( 4r+1 ) ! }\, \left ( \frac{y}{x} \right )^{4r} dk = \int_0^k \frac{1}{ ( 4k-4r ) ! ( 4r+3 ) ! }\, \left ( \frac{y}{x} \right )^{4r} dk [/tex]

The problem is mainly in the factorial part (they are results of binomial coefficients as you may see)

Any help?

P.S. There probably doesn't exist such a k.

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# Integration of factorials

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