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

[harpazo]

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?

 

[Greg]

Is that $(x^2\cos^3(x))^6$? Or $(x^2\cos(x^3))^6$?

 

[harpazo]

Is that $(x^2\cos^3(x))^6$? Or $(x^2\cos(x^3))^6$?

It is (x^2*cos(x^3))^6.

 

[Greg]

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).

 

[MarkFL]

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. :)

 

[harpazo]

There is clearly a typo in this question.

 

[I like Serena]

We can do $(x^2\cos(x^3))^4$ with a combination of substitution, trig sub, and repeated partial integration...

 

[harpazo]

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.