$\int x \ln x d x=$ ?

$\frac{1}{2} x^{2} \ln (x)-\frac{1}{2} x^{2}+C$

$\frac{1}{2} x^{2} \ln (x)+\frac{1}{2} x^{2}+C$

$\frac{1}{2} x^{2} \ln (x)-\frac{1}{4} x^{2}+C$

$\frac{1}{2} x^{2} \ln (x)+\frac{1}{4} x^{2}+C$