Finding the Anti-Derivative of (2+x^2)/(1+x^2): A Scientific Approach

[joeG215]

Homework Statement

f'(x)= (2+x^2)/(1+x^2) Find anti derivative

Homework Equations

The Attempt at a Solution

I attempted to bring the denominator up using (1+x^2)^-1 and i also tried long division to simplify but had no luck...

1/(1+x^2) is the inverse tan derivative, but what can i do from here:

(2+x^2) * 1/(1+x^2) is substitution legal here?

 

[rock.freak667]

Try putting (2+x^2)/(1+x^2) as 2/(1+x^2) + x^2/(1+x^2)

then divide out the second fraction

 

[HallsofIvy]

Or write
$$\frac{2+x^2}{1+ x^2}= \frac{1}{1+x^2}+ \frac{1+ x^2}{1+ x^2}$$

 

[joeG215]

so i would cancel the second term then take the anti derivate to be left with invesre tan of x + x + C .. is this correct?