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:

$u^2 = x+1$

then what would $u^3$ be?

I have come up with:

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

Is that correct?

What i have is:

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

is there an easy way to take the fraction out?

...okay well ive got it like this:

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

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:

$u^2 = x+1$

then what would $u^3$ be?

I have come up with:

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

Is that correct?

What i have is:

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

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

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

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:

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

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:

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

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

Thanks for your help, your right, the answer leaves it in the form to the power 3/2...

Nice job