i have an integral which is of the form of the chebyshev integral

int_u^v P^D * (1-P)^(N-D) dP

where N and D are constants and N>=D

According to the chebyshev integral the solution to this is the incomplete beta function.

My problem is that i need to program a method to solve this. What would you recomend? Simpsons rule? Trapezoid rule? Is there a nice neat analytical solution anyone knows?

Thanks as always for the help