Solve ∫ (4+x) wrt x/1+12x+x^2

$$\int \frac { ( 4 + x ) d x } { 1 + 12 x + x ^ { 2 } }$$

Evaluate

$$\frac{\ln(|x^{2}+12x+1|)}{2}-\frac{\sqrt{35}\ln(\frac{|x+6-\sqrt{35}|}{|x+\sqrt{35}+6|})}{35}+С$$

Differentiate w.r.t. x

$$\frac{\sqrt{35}\left(-sign(x+6-\sqrt{35})x^{3}+|x+6-\sqrt{35}|x^{2}+\sqrt{35}|x+6-\sqrt{35}|x^{2}-\sqrt{35}sign(x+6-\sqrt{35})x^{2}-18sign(x+6-\sqrt{35})x^{2}+12\sqrt{35}x|x+6-\sqrt{35}|-12\sqrt{35}xsign(x+6-\sqrt{35})+47x|x+6-\sqrt{35}|-73xsign(x+6-\sqrt{35})+36\sqrt{35}|x+6-\sqrt{35}|-\sqrt{35}sign(x+6-\sqrt{35})+211|x+6-\sqrt{35}|-6sign(x+6-\sqrt{35})\right)}{35|x+6-\sqrt{35}|\left(x+\sqrt{35}+6\right)\left(x^{2}+12x+1\right)}$$