Primitive of x by Cosine of x/Warning

Primitive of $x \cos x$: Warning
Consider the primitive:


 * $\ds \int x \cos x \rd x$

It is a mistake to use Primitive of Constant Multiple of Function here:


 * $\ds \int x \cos x \rd x = x \int \cos x \rd x$

and thence to deduce:


 * $\ds \int x \cos x \rd x = x \sin x + C$

because $x$ is not a constant in the expression $x \cos x$.