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Evaluate: int(-1)^1(x^3+|x|+1)/(x^2+2|x|...

Evaluate: `int_(-1)^1(x^3+|x|+1)/(x^2+2|x|+1)dx`

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Verified by Experts

The correct Answer is:
`2log_(e)2`
`I=int_(-1)^(1)(x^(3)+|x|+1)/(x^(2)+2|x|+1)dx`
`=int_(-1)^(1)(x^(3))/(x^(2)+2|x|+1)dx+int_(-1)^(1)(|x|+1)/(x^(2)+2|x|+1)dx`
`=0+2int_(0)^(1)((|x|+1)/(|x|+1)^(2))dx=2int_(0)^(1)(dx)/(1+x)`
`=2In(1+x)|_(0)^(1)=2In2`
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