# Integral involving square root -need help

1. Mar 21, 2009

### winbacker

1. The problem statement, all variables and given/known data

integrate sqrt(1-x^-2/3)^1/2.

2. Relevant equations

3. The attempt at a solution

The only thing I can think of is u substitution with u = 1 - x^-2/3. Obviously this cannot work because du differs by more than just a constant.

I guess I need to somehow factor this equation but I do not know how. I think I can pull out an x^1/3 or something but I'm not sure. Any help would be appreciated.

2. Mar 21, 2009

### maze

Whenever you see stuff like that in the square root, always think "Trig Substitution"!

Hint: 1-sin(x)^2 = cos(x)^2.

3. Mar 21, 2009

Do you mean

$$\sqrt{1-x^{-2/3}}$$

or do you mean (as you've written)
$$\sqrt{(1-x^{-2/3})^{1/2}}$$

4. Mar 21, 2009

### winbacker

the first one

5. Mar 21, 2009

### Staff: Mentor

I'm not sure that trig substitution is the way to go in this problem. Trig substitution is a viable alternative for integrals that involve
$$\sqrt{a^2 + x^2}$$
$$\sqrt{a^2 - x^2}$$
$$\sqrt{x^2 - a^2}$$

Maybe it can be made to work in the OP's problem, but I don't see it.