Indefinite Integral?

You can see that the derivative of the denominator is 2(x+1), therefore add 1 to the numerator so that it will have the same form as the derivative and minus 1 so that the function would not be changed. That is: (x+1)dx/(x^2+2x+4) -dx/(x^2+2x+4). We now have two terms. For the first term, use substitution. That is, let u=x^2+2x+4. For the second term, make the denominator a sum of squares by completing the square. The denominator becomes: (x+1)^2+(sq.root of 3)^2. Then use trigonometric substitution, that is, let x+1=sq.root of 3 times tanz. I think you can get the next steps. I hope this helps.