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.