# U substitution

1. May 23, 2012

### robertjford80

1. The problem statement, all variables and given/known data

3. The attempt at a solution

if x2 = u - 1, and if x3 = x2 * x, then x3 should equal (u-1)x, not .5(u-1).

I'm assuming that they got u.5 because (x2+1).5 = (u-1+1).5 which is the same as u^.5

Last edited: May 23, 2012
2. May 23, 2012

### BloodyFrozen

Wait, what did you get?

I ended up getting (in terms of u):

$$\int\frac{1}{2}\sqrt{u}(u-1) du$$

Last edited: May 23, 2012
3. May 23, 2012

### cjc0117

if $u=x^{2}+1$, then what does $dx$ equal?

4. May 23, 2012

### robertjford80

Ok, I see that .5du but I still believe that

if x2 = u - 1, and if x3 = x2 * x, then x3 should equal (u-1)x

so the new answer should be (u-1)x/2 u^.5

5. May 23, 2012

### cjc0117

$dx≠\frac{1}{2}du$

Show how you solve for $dx$.

EDIT: No, I'm sorry. Solve for $du$ if $u=x^{2}+1$.

6. May 23, 2012

### robertjford80

du = 2xdx

du/2 = xdx

7. May 23, 2012

### cjc0117

Yes. So then how can you write $x^{3}dx=x^{2}*xdx$?

8. May 23, 2012

### robertjford80

Ok, I get it now, sort of

9. May 23, 2012

### cjc0117

Don't hold back if you still need help. But just make sure your questions are specific.

10. May 23, 2012

### robertjford80

I think I get it, we'll see if I can apply this technique to future problems, but for now I'm moving on. Thank you for your concern and helping me out.