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Integrate after Pullback

How to integrate a differential for obtained by pullback?

Let say I have calculated the pullback of some differential form, the result is (in latex):


The triple integral is:

sage: integral(integral(integral(rho^2*sin(theta),rho,0,1),theta,0,pi/7),phi,0,pi/5)

But I want this process to be automatic, i.e. not manually write the integrand in the triple integral by myself. I want to be able to extract the integrand from the pullback and put it in the triple integral. I that possible?