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

(C) $\ 2 \log 2 - \text{arccot 3}$

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

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