# Trig Substitution easy right?

1. Nov 9, 2005

### perryben

On this physics problem i need to do a double integral (dx,dy) of 1/sqrt(x^2 + y^2 +z^2). Which looks easy enough at first, until I reallized (after many hours) I cannot figure out how to integrate it. I am sure at this point there is some trig substitution (learned too long ago...), but Im basically lost.

2. Nov 9, 2005

### dextercioby

What's the shape of the domain of integration...?

If it's a circular one (even the $\mathbb{R}^{2}$ can be thought of as a disk of infinite radius), u can convert to polar plane coordinates...

Daniel.

3. Nov 9, 2005

### perryben

Yah, but its a square sheet. thanks though

4. Nov 9, 2005

### dextercioby

In that case, u can depict $y^{2}+z^{2}$ as a constant (wrt "x") $t^{2}$ and use a hyperbolic substitution, in this case

$$x=t\sinh u$$

and then regroup everything and put "y" back and try to integrate the remaining (only of "y" dependent) function.

Daniel.