1. The problem statement, all variables and given/known data
I'm having a hard time setting up a triple integral to find the force of gravity inside a solid sphere. I've done a similar proof in physics before with gravity inside a spherical shell, but it only required a single integral. In this problem the answer must be derived using a triple integral.

3. The attempt at a solution
I believe i found a way to set up the triple integral using spherical coordinates on another physics forum thread, but I don't understand how to get the integrand. Can someone please explain the way the intergrand was derived in the following integral?

THIS PROOF IS FOR INVERSE SQUARE MATH EQUATIONS.
DIVIDE BY DISTANCE r BETWEEN
CENTER OF MASS 1 AND
CENTER OF MASS 2
SQUARED.
YOUR WEIGHT F ON PLANET EARTH SURFACE IS
m1 = YOUR BODY MASS
m2 = PLANET EARTH MASS

r = 6378 KM = 4000 MILES = NOT 0 KM = NOT 0 MILES =
PLANET EARTH RADIUS + HEIGHT OF m1

NOW CALC F = WEIGHT

ALSO APPLIES TO ELECTRIC FORCE
INVERSE SQUARE MATH EQUATION

EXCEPT
GRAVITY IS ONLY ATTRACTION FORCE BUT
ELECTROSTATIC CAN BE
ATTRACTION FORCE OR
REPULSION FORCE

Here's a link to the page on how to use the open practice problem forums: https://www.physicsforums.com/threads/read-me-how-to-use-this-forum.855656/
It's a repository of old unanswered threads that are open for anyone to respond to, without the typical limitations that are generally placed on responses in the homework forums. Many of us in the forum like to solve these problems in our spare time. To keep our knives sharp, so to speak.