Problem with using symbolic integration

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Yasho Bharat Boggarapu
评论： David Goodmanson 2020-5-6
This is my expression
l = 0.0357;
u = 0.9;
p = 5.1;
q =3;
f= ((x-l)^(p-1)*(u-x)^(q-1)/(beta(p,q)*(u-l)^(p+q-1)));
F = (int(f,x,[l x]))
For these values it gives me a solution , where as when I change the value of say q=3.1 , it doesnt solve it . I get this back with some big integers
int((2305843009213693952*(9/10 - x)^(21/10)*(x - 357/10000)^(41/10))/6549555978944313, x, 357/10000, x)
Can anyone help me find the problem?

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David Goodmanson
David Goodmanson 2020-5-6
Hello Yasho,
For any reasonable q, integrating from l to u gives F = 1 by definition of the beta function. When q is an integer, integration from l to an arbitrary x0 gives an answer because symbolic can expand out (u-x)^(q-1) as a polynomial. So for q = 3 you can see a quadratic as part of the answer.
When both p and q are nonintegers and an arbitrary x0 as the upper limit, you have an incomplete beta function which has to be done numerically.
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Yasho Bharat Boggarapu
Yasho Bharat Boggarapu 2020-5-6
But ,I have noticed that beta calculates for any real value of (p,q). Then ,how does it affect the integration ?
David Goodmanson
David Goodmanson 2020-5-6
it allows you to always have an answer for the denominator of the integrand which is good, but it does not affect the conclusion in the previous comment I wrote.

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