Đáp án: $B$
Giải thích các bước giải:
Ta có:
$I=\displaystyle\int \dfrac{x}{x^2+2x+1}dx$
$\to I=\displaystyle\int \dfrac{x}{(x+1)^2}dx$
$\to I=\displaystyle\int \dfrac{x+1-1}{(x+1)^2}dx$
$\to I=\displaystyle\int\dfrac{1}{x+1}-\dfrac{1}{(x+1)^2}dx$
$\to I=\ln|x+1|+\dfrac1{x+1}+C$
$\to \displaystyle\int^1_0 \dfrac{x}{x^2+2x+1}dx=\ln2-\dfrac12$
$\to a=-\dfrac12, b=1, c=0$
$\to 6a+b+c=-2$
$\to B$
