# Homework Help: Anti derivative problem

1. Nov 1, 2008

### joeG215

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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?

Last edited: Nov 1, 2008
2. Nov 1, 2008

### 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

3. Nov 1, 2008

### HallsofIvy

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

4. Nov 1, 2008

### 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?