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March 30th, 2019, 12:36 PM   #1
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Evaluate integral

How to evaluate the integral ?
$\displaystyle \int_{0}^{1} x^{n} e^x dx \; \; $ , $\displaystyle n\in \mathbb{N}$.
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March 30th, 2019, 03:17 PM   #2
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Repeated integrate by parts. $\int_0^1x^ne^xdx=x^ne^x]_0^1-n\int_0^1x^{n-1}e^xdx$ The first term $=e$. Keep going till you hit 0.
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March 31st, 2019, 03:42 PM   #3
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Got the answer like : $\displaystyle (-1)^{n-1}+e\sum_{j=0}^{n} (-1)^{n-j} \frac{n! }{j! }$.
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