Primitive of x by Cosine of x/Proof 1

Theorem

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

Proof

From Primitive of $x \cos a x$:

$\ds \int x \cos a x \rd x = \frac {\cos a x} {a^2} + \frac {x \sin a x} a + C$

The result follows on setting $a = 1$.

$\blacksquare$