INTY<-function(x,theta){
#Set Initial Params
alpha<-theta[1]
lambda<-c(theta[2],theta[3],theta[4])
#Actually integrate
x^alpha*exp(-lambda[2]*x^alpha)*Vectorize(function(x){
gammainc(lambda[1]*x^alpha, 1+1/alpha)[[2]]
})
}

integrate(INTY,theta=theta_high,0,Inf)