Which technique of integration would I use.

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Homework Help Overview

The problem involves the integration of the function ∫(9x^2)/(1+x^6) dx, with participants discussing potential techniques for solving it, particularly focusing on u-substitution.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the use of u-substitution, questioning which function's derivative would simplify the integral. There are attempts to identify appropriate substitutions, with some participants suggesting different forms of u and discussing their effectiveness.

Discussion Status

The discussion is active, with various approaches being proposed. Some participants provide guidance on potential substitutions, while others reflect on their attempts and the challenges faced. There is no explicit consensus, but several lines of reasoning are being explored.

Contextual Notes

Participants mention specific substitutions that did not yield results, indicating a trial-and-error approach. The original poster expresses uncertainty about the u-substitution method, which is a common technique in integration problems.

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Homework Statement


∫(9x^2)/(1+x^6 ) dx I was thinking of using U substitution but I can't figure it out.


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The Attempt at a Solution

 
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You actually could use u-substitution here. You just need to figure out...

what function would have as it's derivative something that will cancel out when I u-sub?

Now, what seems most easily canceled out here is the x^2 dx... so maybe if we had something like

[tex]du=x^2 dx[/tex]

with an appropriate coefficient, it could make the integral a lot easier.
 
What have you tried? There aren't a lot of possibilities.
 
I tried to let u=x^6 which made du 6x^5. This didn't get me anywhere. I also tried letting u= 9x^2 and that also got me nowhere.
 
That's because it won't work if you do that. Try letting du = 9x^2 dx instead. That will get you farther. You just need to solve for u instead of solving for du.
 
Oh alright I've got it now! Thanks so much.
 

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