How to integrate int x/(x^2+1)dx

[naspek]

$$\int{\left(\frac{x}{x^2 + 1}\right)\,dx}$$

how to integrate?
i know $$\int{\left(\frac{1}{x^2 + 1}\right)\,dx}$$
is tan^-1 x + C

how am i going to start answering this question

 

[rock.freak667]

try substituting u=x²+1, du=?

 

[naspek]

try substituting u=x²+1, du=?

meaning.. i should u integration by substitution?

 

[Bohrok]

Yes, try the u substitution.

 

[naspek]

got it..
1/2 ln |x^2 + 1| + C

correct?

 

[Bohrok]

That's right. One thing though: since x² + 1 is always greater than 0, no absolute values are needed.