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Evaluate int(x+2)/((x^2+3x+3)sqrt(x+1))+...

Evaluate `int(x+2)/((x^2+3x+3)sqrt(x+1))+C`

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`int(x+2)/((x^2+3x+3)sqrt(x+1)) dx`
`x+1=t^2=>dx=2tdt`
`I=2int(x+1+1)/((x^2+2x+x+2+1)sqrt(x+1))`
`=2int(x+1+1)/(((x+1)^2+x+2)sqrt(x+1))`
`2 int frac{t^2+1}{t^4+t^2+1}dt`
`=2 int frac{1+(frac{1}{t})^2}{(t-frac{1}{t})^2+3}dt`
`=2/sqrt 3tan^(-1)(frac{t-1/t}{sqrt 3})+C`
`=2/sqrt 3 tan^(-1) frac{x}{sqrt(3(x+1))}+C`
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