Integrating By Parts: Is 4 Times Best for \int {x^4 e^x dx}?

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Homework Help Overview

The discussion revolves around evaluating the integral \(\int {x^4 e^x dx}\) and whether integrating by parts four times is the most efficient method.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the necessity of integrating by parts four times and consider the potential for a reduction formula in the case of a definite integral.

Discussion Status

Some participants suggest that integrating by parts four times is required, while others introduce the idea of a reduction formula for definite integrals, indicating a productive exploration of different approaches.

Contextual Notes

There is mention of a different question regarding definite integrals, which may imply varying methods depending on the integral's limits.

danago
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Hi. When evaluating an integral such as:

[tex] \int {x^4 e^x dx} [/tex]

Is integrating by parts 4 times the best method, or is there a more efficient way?

Thanks in advance,
Dan.
 
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I think you are going to have to do parts 4 times.
 
Well if the problem was a definite integral for example say:
[itex]\int_{0}^{1} x^4e^x dx[/itex]

you could easily make a reduction formula for easy calculations. But that is a different question altogether. As previously stated you would have to integrate by parts at 4 times
 
Alright, thanks for the replies guys :smile:
 

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