Let $r$ and $s$ be two strictly positive natural integers such that $r \geqslant s$. Let $y \in ] 0,1 [$. Justify that the function $$x \mapsto \frac { x ^ { r } y ^ { s } } { 1 - x y }$$ is integrable on $[ 0,1 ]$.
Let $r$ and $s$ be two strictly positive natural integers such that $r \geqslant s$.
Let $y \in ] 0,1 [$. Justify that the function
$$x \mapsto \frac { x ^ { r } y ^ { s } } { 1 - x y }$$
is integrable on $[ 0,1 ]$.