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Question: integral evaluation

Question:integral evaluation

Scimann 511 Maple
integral
April 20 2009
0

What's the easierst way to show (with maple) the integral below evaluates (for alphas, betas>0) to the expression given after it? Thanks.



(int(x^(-1+alpha[1])*(1-x)^(-1+beta[1])*ln(x^(alpha[1]-alpha[2])*(1-x)^(beta[1]-beta[2])*Beta(alpha[2], beta[2])/Beta(beta[1], alpha[1])), x = 0 .. 1))/Beta(beta[1], alpha[1])

ln(Beta(alpha[2], beta[2])/Beta(beta[1], alpha[1]))-(-alpha[1]+alpha[2])*Psi(alpha[1])-(beta[2]-beta[1])*Psi(beta[1])+(alpha[2]-alpha[1]+beta[2]-beta[1])*Psi(alpha[1]+beta[1])
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