# How To Integrate This?

1. Jun 16, 2013

### vee6

How to integrate below?

$$\int \sqrt{\frac{r^{2}-x^{2}+x^{2}}{r^{2}-x^{2}}} dx$$

neither if u = r^2 - x^2 nor u = x^2 will get the result.

2. Jun 16, 2013

### Staff: Mentor

Try u=x/r, and simplify, it should become a standard integral (solvable with formulas, or with a trigonometric substitution)

3. Jun 16, 2013

### HallsofIvy

Is this really what you meant? Since $-x^2+ x^2= 0$ the is exactly the same as
$$|r|\int \frac{1}{\sqrt{r^2- x^2}}dx$$

The substitution x= sin(t) would be a stadard technique for this.