I have to calculate the integrale of $f$ on $T$.
I think it is a triple integrale, but I didn't manage to solve it.
$$ f(x,y,z)=\frac{1}{1+x+y+z} $$ $$ T=\{(x, y, z)\in{(\mathbb R^+)^3}:||(x, y, z)||_1\le{1}\} $$ With $$ T=\{(x, y, z)\in{(\mathbb R^+)^3}:0\le{x}\le{1},0\le{y}\le{1-x}, 0\le{z}\le{1-x-y}\} $$
I try to integrate first by $z$, then $y$, then $x$, is it good way ? I have to use spherical coordinate or not ? I have find this integral to solve : $$ \int\limits_{0}^{1} \int\limits_{0}^{1-x} \int\limits_{0}^{1-x-y} f(x,y,z)\mathrm dz\mathrm dy\mathrm dx $$
