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Evaluate: int(2x)/((x^2+1)(x^2+2))\ dx...

Evaluate: `int(2x)/((x^2+1)(x^2+2))\ dx`

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`I=int frac{2 x}{(x^{2}+1)(x^{2}+2)}`

`frac{1}{(x^{2}+1)(x^{2}+2)}=frac{A}{x^{2}+1}+frac{B}{x^{2}+2}`

`=frac{A(x^{2}+2)+B(x^{2}+1)}{(x^{2}+1)(x^{2}+2)}`

`Rightarrow A+B=0, quad 2 A+B=1`

`Rightarrow A=-B, quad-2 B+B=1`

`Rightarrow B=-1` and `A=1`

`Rightarrow I=int(frac{1}{(x^{2}+1)}-frac{1}{(x^{2}+2)}) 2 x d x`

`I=int(frac{2 x d x}{(x^{2}+1)}-frac{2 x d x}{(x^{2}+2)})`

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