Résoudre ∫ log_{2}(x^2+3x+1) wrt x

$$\int \log _ { 2 } ( x ^ { 2 } + 3 x + 1 ) d x$$

Évaluer

$$\frac{2x\ln(x^{2}+3x+1)+3\ln(x^{2}+3x+1)-4x-16\sqrt{5}\ln(\frac{|2x+3-4\sqrt{5}|}{|2x+4\sqrt{5}+3|})}{2\ln(2)}+С$$

Différencier w.r.t. x

$$\frac{4|2x+3-4\sqrt{5}|x^{3}\ln(x^{2}+3x+1)+8\sqrt{5}|2x+3-4\sqrt{5}|x^{2}\ln(x^{2}+3x+1)+18|2x+3-4\sqrt{5}|x^{2}\ln(x^{2}+3x+1)+24\sqrt{5}x|2x+3-4\sqrt{5}|\ln(x^{2}+3x+1)+22x|2x+3-4\sqrt{5}|\ln(x^{2}+3x+1)+8\sqrt{5}|2x+3-4\sqrt{5}|\ln(x^{2}+3x+1)+6|2x+3-4\sqrt{5}|\ln(x^{2}+3x+1)-64\sqrt{5}sign(2x+3-4\sqrt{5})x^{3}+32\sqrt{5}|2x+3-4\sqrt{5}|x^{2}-288\sqrt{5}sign(2x+3-4\sqrt{5})x^{2}-640sign(2x+3-4\sqrt{5})x^{2}+96\sqrt{5}x|2x+3-4\sqrt{5}|-352\sqrt{5}xsign(2x+3-4\sqrt{5})+10x|2x+3-4\sqrt{5}|-1920xsign(2x+3-4\sqrt{5})+52\sqrt{5}|2x+3-4\sqrt{5}|-96\sqrt{5}sign(2x+3-4\sqrt{5})+15|2x+3-4\sqrt{5}|-640sign(2x+3-4\sqrt{5})}{2\ln(2)|2x+3-4\sqrt{5}|\left(2x+4\sqrt{5}+3\right)\left(x^{2}+3x+1\right)}$$