What is $\int \frac{6x+8}{3x^2+6x+2}dx$?
Answer & explanation
Correct answer: option 1
$\int \frac{6x+8}{3x^2+6x+2}dx=\int \frac{6x+6}{3x^2+6x+2}dx+\int \frac{2}{3x^2+6x+2}dx=\int \frac{d(3x^2+6x+2)}{3x^2+6x+2}+\int \frac{2}{3{(x+1)^2-1/3}}dx=\ln(3x^2+6x+2)+2/3\ln |\frac{x+1-1/ 3}{x+1+1/ 3}|+C$