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 option(s) is 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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