Expert: Paul Klarreich - 10/2/2009

Question
Hi Paul,
I am trying to find the indefinite integral of
{x^(1/3)-x^(-1/3)}dx.

I got an answer of 3/2{(x^(1/3)-x^(-1/3)}^2+c.
Is it correct?

Appreciate your help once again.
Many thanks.

Answer
Questioner: Libby
Country: Singapore
Category: Calculus
Private: No
Subject: Indefinite Integrals
Question: Hi Paul,
I am trying to find the indefinite integral of
{x^(1/3)-x^(-1/3)}dx.

I got an answer of 3/2{(x^(1/3)-x^(-1/3)}^2+c.
Is it correct?

Appreciate your help once again.
Many thanks.
........................................
Hi, Libby,

Sorry, but I think you went wrong somewhere.

{
| [x^(1/3) - x^(-1/3)] dx =
}

 x^(4/3)      x^(2/3)
----------- - ---------- =
  4/3           2/3

3x^(4/3)      3x^(2/3)
----------- - ---------
  4              2


This does not look like your answer.  Maybe we can do something.

Your answer was:

3/2{ x^(1/3) - x^(-1/3) }^2

3/2{ x^(2/3) + x^(-2/3) - 2 }

Close, but still no good.  You are not going to get a negative exponent here.

Send me what you did and we'll try to find where you went off.