# Using trig identity to simplify?

I have this equation 1/(r^2+l^2)^(3/2) and I need to integrate it quickly. My first thought is using this integral formula 1/(1+x^2)^(3/2)=x/sqrt(1+x^2) but how exactly do I get my equation into that form?

Simon Bridge
Homework Helper
$$\int \frac{dr}{(r^2+l^2)^{3/2}}$$

You are thinking too much of formulas and not enough of algebra.
What happens if you put r=lx?

I'm not sure what you mean by what happens. Like, do the integral when r^2=l^2*x^2?

pwsnafu
I'm not sure what you mean by what happens. Like, do the integral when r^2=l^2*x^2?

He means "do the substitution and write down what you get".

Ok I do get a right answer doing that way. Im confused though, how can I just sub in lx? I understand if we divide or multiply to shift the variables around but I'm confused on this subbing thing.

Office_Shredder
Staff Emeritus
Gold Member
Ok I do get a right answer doing that way. Im confused though, how can I just sub in lx? I understand if we divide or multiply to shift the variables around but I'm confused on this subbing thing.

Integration by substitution, the integration technique, as opposed to integration by randomly plugging in other things

Oh I went through it again and its simple u sub nevermind haha.

Simon Bridge