Integrating (x^2cosx^3)^6: A Review of Techniques

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Discussion Overview

The discussion revolves around the integration of the expression (x^2cos(x^3))^6. Participants explore various techniques for integration and express uncertainty regarding the formulation of the problem.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant suggests using integration by parts, substitution, trigonometric substitution, or partial fraction decomposition for the integration.
  • Multiple participants seek clarification on the expression, questioning whether it is (x^2cos^3(x))^6 or (x^2cos(x^3))^6.
  • Some participants express doubt about the problem's formulation, suggesting there may be a typo or an issue with the expression as presented.
  • One participant mentions that they have attempted to work through the problem but found it likely too complex, indicating a preference for a simpler expression like (x^2cos(x^3))^4 instead.

Areas of Agreement / Disagreement

Participants generally agree that there may be a typo in the original problem statement, but there is no consensus on how to proceed with the integration or on the correct interpretation of the expression.

Contextual Notes

Participants express uncertainty regarding the integration techniques applicable to the original expression and the potential impact of a typo on the problem's complexity.

harpazo
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Integrate this (x^2cosx^3)^6.

I absolutely forgot how to integrate several calculus 2 integrals.

Integration by parts?

Substitution?

Trig sub?

Partial fraction decomposition?
 
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Is that $(x^2\cos^3(x))^6$? Or $(x^2\cos(x^3))^6$?
 
greg1313 said:
Is that $(x^2\cos^3(x))^6$? Or $(x^2\cos(x^3))^6$?

It is (x^2*cos(x^3))^6.
 
Hi Harpazo. There doesn't seem to be anything nice about it. Maybe there's a typo or something - or maybe I'm missing something (but I doubt it).
 
greg1313 said:
Hi Harpazo. There doesn't seem to be anything nice about it. Maybe there's a typo or something - or maybe I'm missing something (but I doubt it).

I played with it a few times myself, and also came to the conclusion that there is likely a typo in the problem as given to the OP. :)
 
There is clearly a typo in this question.
 
We can do $(x^2\cos(x^3))^4$ with a combination of substitution, trig sub, and repeated partial integration...
 
I like Serena said:
We can do $(x^2\cos(x^3))^4$ with a combination of substitution, trig sub, and repeated partial integration...

Forget it. This problem is too involved.
 

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