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Y=∫012x2+3x+3(x+1)(x2+2x+2)dx Y = \int _{ 0 }^{ 1 }{ \frac { 2{ x }^{ 2 }+3x+3 }{ (x+1)({ x }^{ 2 }+2x+2) } } dx Y=∫01(x+1)(x2+2x+2)2x2+3x+3dx
Which of the following options are equal to Y?Y?Y?
(A) π4+2log2−arctan2\ \frac { \pi }{ 4 } +2\log2-\arctan { 2 } 4π+2log2−arctan2
(B) π4+2log2−arctan13\ \frac { \pi }{ 4 } +2\log2-\arctan {\frac{1}{3}} 4π+2log2−arctan31
(C) 2log2−arccot 3\ 2 \log 2 - \text{arccot 3} 2log2−arccot 3
(D) −π4+log4+arccot 2\ -\frac{\pi}{4}+\log4+\text{arccot 2} −4π+log4+arccot 2
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