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

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SUMMARY

The discussion centers on the integration of the expression (x^2cos(x^3))^6. Participants express uncertainty regarding the expression's complexity and suggest that it may contain a typo. They conclude that a more manageable expression, such as (x^2cos(x^3))^4, could be integrated using techniques like substitution, trigonometric substitution, and repeated integration by parts. Ultimately, the consensus is that the original problem is overly complicated and likely erroneous.

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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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