Is U Substitution the Key to Solving Tricky Integration Problems?

[robertjford80]

Homework Statement

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

 

[BloodyFrozen]

Wait, what did you get?

I ended up getting (in terms of u):

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

 

[cjc0117]

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

 

[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

 

[cjc0117]

$dx≠\frac{1}{2}du$

Show how you solve for $dx$.

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

 

[robertjford80]

du = 2xdx

du/2 = xdx

 

[cjc0117]

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

 

[robertjford80]

Ok, I get it now, sort of

 

[cjc0117]

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

 

[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.