Primitive of x by Logarithm of x/Proof 2

Theorem

$\ds \int x \ln x \rd x = \frac {x^2} 2 \paren {\ln x - \frac 1 2} + C$

Proof

From Primitive of $x^m \ln x$:

$\ds \int x^m \ln x \rd x = \frac {x^{m + 1} } {m + 1} \paren {\ln x - \frac 1 {m + 1} } + C$

The result follows by setting $m = 1$.

$\blacksquare$