Using trig identity to simplify?

1. May 12, 2013

Typhon4ever

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?

2. May 12, 2013

Simon Bridge

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

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

3. May 12, 2013

Typhon4ever

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

4. May 12, 2013

pwsnafu

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

5. May 12, 2013

Typhon4ever

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.

6. May 12, 2013

Office_Shredder

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

7. May 12, 2013

Typhon4ever

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

8. May 13, 2013

Simon Bridge

(My emphasis.)
If I said "substitute r=lu" you'd have been fine?

You have to look for these things ...
...the way forward will not normally look like some formula you've memorized.

Anyway you go there - well done.