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 YY ?

  • (A): π4+2log2arctan2\dfrac { \pi }{ 4 } +2\log2-\arctan { 2 }
  • (B): π4+2log2arctan13\dfrac { \pi }{ 4 } +2\log2-\arctan {\frac{1}{3}}
  • (C): 2log2arccot 32 \log 2 - \text{arccot 3}
  • (D): π4+log4+arccot 2-\dfrac{\pi}{4}+\log4+\text{arccot 2}
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