Efficient U-Substitution for (x^2)(sinx)/(1+x^6)

[nameVoid]

[ ( x^2 ) ( sinx ) ] / (1 + x^6)

 

[cristo]

17.4

 

[Mark44]

Cristo, I get 42. You might have forgotten to multiply by Hooker's constant (= 2.413793103).

 

[jbunniii]

Don't listen to these clowns. The answer you seek is

[ ( u^2 ) ( sinu ) ] / (1 + u^6)

 

[Mark44]

Don't listen to these clowns. The answer you seek is

[ ( u^2 ) ( sinu ) ] / (1 + u^6)

That's an extremely useful substitution in those cases where you find the given variable esthetically displeasing for some reason.

For all other cases, not so much.

 

[Mark44]

nameVoid,
If you're still out there, you would have gotten more serious (and helpful) responses if you had given us the complete problem. We can infer that this is an integration problem, although there was no indication of that in what you wrote. Also, if you want help, show us what you've tried.

The integral looks to me like it could be done using integration by parts in this way:
u = cos x
$$dv = \frac{x^2 dx}{1 + x^6}$$

To find v, you'll have to integrate dv, which involves a substitution w = x³, dw = 3x²dx. I haven't worked it out, but this is what I would try first.