Using trig identity to simplify?

[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?

 

[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?

 

[Typhon4ever]

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".

 

[Typhon4ever]

Ok I do get a right answer doing that way. I am 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]

Ok I do get a right answer doing that way. I am 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

 

[Typhon4ever]

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

 

[Simon Bridge]

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

(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.