Triple integral of symbolic function

I am trying to evaluate triple integral of a symbolic function.

Where the symbolic function is given as below:

func=r.^2.*sin(phi).*(r.^2.*cos(phi).^2 + r.*cos(theta).*sin(phi) + r.*sin(phi).*sin(theta))

The triple integral equation is given as below:

Since this is symbolic function integral, it should not be calculating the integral, instead return the value of the integral.

Which function within matlab should I be using?

and how to use that function?

Answer 1

[Star Strider]

Try this —

syms phi r theta r0 r1 phi0 phi1 theta0 theta1  
sympref('AbbreviateOutput',false);
func(r,phi,theta) = r.^2.*sin(phi).*(r.^2.*cos(phi).^2 + r.*cos(theta).*sin(phi) + r.*sin(phi).*sin(theta))

func(r, phi, theta) = 

intr = int(func, r, r0, r1)

intr(phi, theta) = 

intphi = int(intr, phi, phi0, phi1)

intphi(theta) = 

inttheta = int(intphi, theta, theta0, theta1)

inttheta = 

int3 = simplify(inttheta, 500)

int3 = 

Make appropriate changes to get the desired result.

.