Why is $x^5 \sin x$ an odd function? Why is $x^5 \sin x$ an odd function? 
Is the result just wrong? Because $f(-x)= (-x)(-x)(-x) \sin(-x) =  (-x)(-x)(-x)(-x)(-x) (-\sin x) = (-x^5)(-\sin x) = x^5 \sin x$

If $f(x) = x^5 \sin x$, then
$$f(-x) = (-x)^5 \sin (-x) = -x^5 \left( - \sin x\right) = x^5 \sin x = f(x),$$
and so $f$ is actually even.
