Integration @ 02

Calculus Level 5

$Y = \int _{ 0 }^{ 1 }{ \frac { 2{ x }^{ 2 }+3x+3 }{ (x+1)({ x }^{ 2 }+2x+2) } } dx$

Which of the following options are equal to $Y?$

(A) $\ \frac { \pi }{ 4 } +2\log2-\arctan { 2 }$

(B) $\ \frac { \pi }{ 4 } +2\log2-\arctan {\frac{1}{3}}$

(D) $\ -\frac{\pi}{4}+\log4+\text{arccot 2}$

(A), (B) and (C) (A), (B), (C) and (D) (A), (B) and (D) (A) and (C) (A), (C) and (D) (A) and (D) (B) and (C) (B), (C) and (D)