Answer
$$\int x\,lnx\,dx=\frac{x^{2}lnx}{2}-\frac{x^{2}}{4}+C$$
Work Step by Step
$${(\frac{x^{2}lnx}{2})}'=xlnx+\frac{x}{2}$$
$$\int x\,lnx\,dx=\frac{x^{2}lnx}{2}-\frac{1}{2}\int x\,dx$$
$$=\frac{x^{2}lnx}{2}-\frac{x^{2}}{4}+C$$
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