Integral ∫dr/√((1/(R+r))-(1/R))

[armin.hodaie]

Homework Statement

∫dr/√((1/(R+r))-(1/R))

Homework Equations

The Attempt at a Solution

 

[gb7nash]

Is the problem $\int \frac{dr}{\sqrt{(\frac{1}{R}+r)-(\frac{1}{R})}}$?

If it is, try to simplify the denominator before trying to take the integral.

 

[armin.hodaie]

no,i type it wrong
∫dr/√((1/(R+r))-(1/R))

 

[Ray Vickson]

Homework Statement

∫dr/√((1/(R+r))-(1/R))

Homework Equations

The Attempt at a Solution

So, is your integral
$$\int \frac{dr}{\sqrt{\frac{1}{R+r}-\frac{1}{R}}} ?$$
If so, re-write it by first expressing
$$\frac{1}{R+r}-\frac{1}{R}$$
as a simple rational expression. You should end up with an integrand of the form
$$\sqrt{\frac{ar+b}{cr+d}}.$$

RGV