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 March 30th, 2019, 11:36 AM #1 Senior Member   Joined: Dec 2015 From: iPhone Posts: 486 Thanks: 75 Evaluate integral How to evaluate the integral ? $\displaystyle \int_{0}^{1} x^{n} e^x dx \; \;$ , $\displaystyle n\in \mathbb{N}$.
 March 30th, 2019, 02:17 PM #2 Global Moderator   Joined: May 2007 Posts: 6,732 Thanks: 689 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. Thanks from topsquark and idontknow
 March 31st, 2019, 02:42 PM #3 Senior Member   Joined: Dec 2015 From: iPhone Posts: 486 Thanks: 75 Got the answer like : $\displaystyle (-1)^{n-1}+e\sum_{j=0}^{n} (-1)^{n-j} \frac{n! }{j! }$.

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