I-need-help-0-1-x-n-e-x-2-2-dx-n-N-

Question Number 217794 by yamane last updated on 21/Mar/25

I n e e d h e l p

\int_{0}^{1} x^{n} e - \frac{x^{2}}{2} d x (n \in N)

Answered by Wuji last updated on 21/Mar/25

\int_{0}^{1} x^{n} e - \frac{x^{2}}{2} d x (n \in N)

e \int_{0}^{1} x^{n} - \frac{x^{2}}{2} d x \Rightarrow e (\int_{0}^{1} x^{n} d x) - \frac{1}{2} \int_{0}^{1} x^{2} d x

e (\frac{1}{n + 1}) - \frac{1}{2} (\frac{1}{3})

e (\frac{1}{n + 1}) - \frac{1}{6}

\frac{e}{n + 1} - \frac{1}{6}

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