What is $\int \frac{6x+8}{3x^2+6x+2}dx$?

$\ln(3x^2+6x+2)+2/3\ln |\frac{x+1-1/\sqrt 3}{x+1+1/\sqrt 3}|+C$ $\ln(3x^2+6x+2)+2/3\ln |\frac{x+1+1/\sqrt 3}{x+1-1/\sqrt 3}|+C$ $\ln(3x^2+6x+2)+\ln |\frac{x+1-1/\sqrt 3}{x+1+1/\sqrt 3}|+C$ $2/3\ln |\frac{x+1-1/\sqrt 3}{x+1+1/\sqrt 3}|+C$

$\ln(3x^2+6x+2)+2/3\ln |\frac{x+1-1/\sqrt 3}{x+1+1/\sqrt 3}|+C$

$\int \frac{6x+8}{3x^2+6x+2}dx=\int \frac{6x+6}{3x^2+6x+2}dx+\int \frac{2}{3x^2+6x+2}dx=\int \frac{d(3x^2+6x+2)}{3x^2+6x+2}+\int \frac{2}{3{(x+1)^2-1/3}}dx=\ln(3x^2+6x+2)+2/3\ln |\frac{x+1-1/\sqrt 3}{x+1+1/\sqrt 3}|+C$