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- Thread starter minase
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Easy, use integration by part, show the following relationship

[tex] \int x^n e^x dx = x^ne^x -n\int x^{n-1}e^x dx [/tex]

Then use the recurrence relation on [tex] \int x^{n-1} e^x dx [/tex].

You will get

[tex] \int x^{n} e^x} dx = \sum _{i=0} ^{n} (-1)^i\frac{n!}{(n-i)!}e^xx^{n-i} [/tex]

[tex] \int x^n e^x dx = x^ne^x -n\int x^{n-1}e^x dx [/tex]

Then use the recurrence relation on [tex] \int x^{n-1} e^x dx [/tex].

You will get

[tex] \int x^{n} e^x} dx = \sum _{i=0} ^{n} (-1)^i\frac{n!}{(n-i)!}e^xx^{n-i} [/tex]

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Gib Z

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