# U substitution

1. May 27, 2009

### nameVoid

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

2. May 27, 2009

### cristo

Staff Emeritus
17.4

3. May 27, 2009

### Staff: Mentor

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

4. May 27, 2009

### jbunniii

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

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

5. May 28, 2009

### Staff: Mentor

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.

6. May 28, 2009

### Staff: Mentor

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.