1.82: Product rule and reverse integration

0606/13/O/N/19 — Question 5 · 5 marks

(i)
Differentiate (x2+3)ln(x2+3)(x^{2} + 3)\ln(x^{2} + 3) with respect to xx.
[3]
(ii)
Hence find xln(x2+3)dx\displaystyle\int x\ln(x^{2} + 3)\,\mathrm{d}x.
[2]