Which technique of integration would I use.

[mickellowery]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[Char. Limit]

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

$$du=x^2 dx$$

with an appropriate coefficient, it could make the integral a lot easier.

 

[Mark44]

What have you tried? There aren't a lot of possibilities.

 

[mickellowery]

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.

 

[Char. Limit]

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.

 

[Mark44]

Try u = x^3

 

[mickellowery]

Oh alright I've got it now! Thanks so much.