Integration @ 02

Calculus Level 5

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

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

(A)  π4+2log2arctan2\ \frac { \pi }{ 4 } +2\log2-\arctan { 2 }

(B)  π4+2log2arctan13\ \frac { \pi }{ 4 } +2\log2-\arctan {\frac{1}{3}}

(C)  2log2arccot 3\ 2 \log 2 - \text{arccot 3}

(D)  π4+log4+arccot 2\ -\frac{\pi}{4}+\log4+\text{arccot 2}

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