1. ## Route cubed

Hello there,

Doing a bit of integration using substitution and when i come to sub back in i have come across an interesting case:
Lets say that:

$\displaystyle u^2 = x+1$

then what would $\displaystyle u^3$ be?

I have come up with:

$\displaystyle (x+1)\sqrt{x+1}$

Is that correct?

What i have is:

$\displaystyle u^3(\frac{2}{5}u^2 - \frac{2}{3})$

is there an easy way to take the fraction out?

...okay well ive got it like this:

$\displaystyle \frac{1}{15}u^3(6u^2-10)$

is that right?

2. Originally Posted by darksupernova
Hello there,

Doing a bit of integration using substitution and when i come to sub back in i have come across an interesting case:
Lets say that:

$\displaystyle u^2 = x+1$

then what would $\displaystyle u^3$ be?

I have come up with:

$\displaystyle (x+1)\sqrt{x+1}$

Is that correct?

What i have is:

$\displaystyle u^3(\frac{2}{5}u^2 - \frac{2}{3})$

is there an easy way to take the fraction out?
I would think there are two possibilities for u^3, the one you gave, and the additive inverse.

Edit: You added the last three lines afterwards so I didn't see them.

Are you saying that

$\displaystyle u^3(\frac{2}{5}u^2 - \frac{2}{3}) + C$

is the result of your integration on u du?

Any rate, it's probably easiest to write, for example, (x+1)^(3/2) and avoid the trouble of all the radical signs.

would that be:

$\displaystyle (x+1)^\frac{3}{2}$

4. Originally Posted by darksupernova
Just the value times negative one.

I edited my first post to reflect your updated post.

Edit: Ah, there's more now..

Originally Posted by darksupernova
...okay well ive got it like this:

$\displaystyle \frac{1}{15}u^3(6u^2-10)$

is that right?
I'm not sure what kind of simplification you're going for, but what you did was valid.