<s>[INST] Integration based on beta function 
I am getting the value of first integration using the beta function, but I am not able to find the second one. Please help
 [/INST] $\because$ $\int_0^1\dfrac{x^{a-1}(1-x)^{b-1}}{(z+x)^{a+b}}~dx=\dfrac{B(a,b)}{(z+1)^az^b}$ as https://dlmf.nist.gov/5.12 stated,
$\therefore$ $\int_0^1\dfrac{x^\frac{5}{2}(1-x)^\frac{7}{2}}{(3+x)^8}~dx=\int_0^1\dfrac{x^{\frac{7}{2}-1}(1-x)^{\frac{9}{2}-1}}{(3+x)^{\frac{7}{2}+\frac{9}{2}}}~dx=\dfrac{B\left(\frac{7}{2},\frac{9}{2}\right)}{4^\frac{7}{2}3^\frac{9}{2}}$
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