Help with Integrating: x^11 e^x / 5x^6

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Homework Help Overview

The problem involves integrating the expression x^11 e^x / 5x^6, which simplifies to -1/5 ∫ x^5 e^x dx. The discussion centers around the methods of integration, particularly integration by parts.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to simplify the integral and apply integration by parts, but expresses confusion about the outcome. Some participants question the correctness of the integration steps and suggest that further applications of integration by parts may be necessary.

Discussion Status

Participants are exploring the integration process, with some suggesting that integration by parts is the most effective method. There is acknowledgment of the original poster's confusion, and encouragement is provided, but no consensus on an alternative method has been reached.

Contextual Notes

There is a mention of the potential complexity of the integration process, with participants noting that multiple applications of integration by parts may be required. The original poster expresses concern about their approach, indicating a need for clarification.

confused88
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Homework Statement


Can Someone Please Help me integrate the following please...


Homework Equations


- [tex]\int[/tex] x^11 e^x [tex]/[/tex] 5x^6


The Attempt at a Solution


firstly i simplified it to...

-1/5 [tex]\int[/tex] x^5 e^x [tex]/[/tex] 5

Then i did integration by parts,
u = x^5, du = 5x^4, v= e^x, dv= e^x

So i got,

-1/5 [ x^5 e^x [tex]\int[/tex] e^x 5x^4 + C

-1/5 [x^5 e^x - x^5 e^x + C ]

= -1/5C


And this seems insanely wrong :(

Please let me know what I'm doing wrong
 
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[tex]\int[/tex]5x[tex]^{4}[/tex]e[tex]^{x}[/tex]dx [tex]\neq[/tex] x[tex]^{5}[/tex]e[tex]^{x}[/tex]+C

You're going to have to use integration by parts a few more times...
 
Is there an easier way to do it? Or is integration by parts the only way?
 
I'd say integration by parts is the best way if not the only way. It will be good practice! Good luck and remember to have fun :)
 
hehe okies thanks!
 

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