3.38: Exact integral ∫02ex2/2 dx\int_0^2 e^{x^{2}/2}\,\mathrm{d}x form

0606/13/M/J/24 — Question 4 · 5 marks

Find ∫02xex2/2 dx\displaystyle\int_{0}^{2} x e^{x^{2}/2}\,\mathrm{d}x, giving your answer in exact form.
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