# Math Help - Integration Question

1. ## Integration Question

I'm wondering how I can integrate y/(1 + y^2) ... I'm sure there is some trick to doing this but I can't figure it out at the moment.

2. I guess it's $\int{\frac{y}{1+y^2}dy}$ isn't it?

See it this way: $\int{\frac{y}{1+y^2}dy}=\frac{1}{2}\cdot{\int{\fra c{(1+y^2)'}{1+y^2}dy}}$

3. More generally:

$\int {\frac{{f'(x)}}
{{f(x)}}\,dx} = \ln \left| {f(x)} \right|+k\,,\forall f(x) \ne 0$

4. Originally Posted by PaulRS
I guess it's $\int{\frac{y}{1+y^2}dy}$ isn't it?

See it this way: $\int{\frac{y}{1+y^2}dy}=\frac{1}{2}\cdot{\int{\fra c{(1+y^2)'}{1+y^2}dy}}$

So, the answer would be 1/2 * ln|1 + y^2| ??

I suppose that works now that I works backwards and derive it. Still, that's a pretty tricky question to ask. =/ Thanks guys!

5. Yes.

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You can remove the bars 'cause $1+y^2$ is always positive.