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 $x \cos x$.

Sources

• 1945: A. Geary, H.V. Lowry and H.A. Hayden: Advanced Mathematics for Technical Students, Part I ... (previous) ... (next): Chapter $\text {III}$: Integration: Three rules for integration: $\text {I}$