I'm asked in an exercise to calculate the mass of the ball $x^2+y^2+z^2=1$ with a density of $e^x+e^y+e^z$ at a given point. We've only learned triple integration with Cartesian coordinates so far so I'm trying to set up a triple integral using those. But I get sort of stuck in figuring out how I want to set up the integral.
My first thought was, I should have one coordinate, say z, go from $-1$ to $1$, y from $-\sqrt{1-z^2}$ to $\sqrt{1-z^2}$ and x from $-\sqrt{1-y^2-z^2}$ to $\sqrt{1-y^2-z^2}$. But the resulting integral turned out to be hard to calculate and the answer seems wrong.
Any tips would be appreciated :). Thanks!