# Integral involving square root -need help

## Homework Statement

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

## 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.

Related Calculus and Beyond Homework Help News on Phys.org
Whenever you see stuff like that in the square root, always think "Trig Substitution"!

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

Homework Helper
Do you mean

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

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

the first one

Mark44
Mentor
Whenever you see stuff like that in the square root, always think "Trig Substitution"!

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