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User defined function

I'm working with beta distribution and its integral. A straightforward integral of beta distribution would return the hypergeometric form of the incomplete beta function. This makes my results very messy and difficult to work with. I have been able to define a function class IncBeta as

def D_t(self, t, z, w, **kwds):
    return t^(z-1)*(1-t)^(w-1)#/beta(z, w)

IncBeta=function('IncBeta', nargs=3, derivative_func=D_t, latex_name='I_x')

Is there a way that I can define an inverse function class of the above and tell Sage the integral of that inverse function leads to IncBeta?