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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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`"Let I " =int (2x)/((x^(2)+1)(x^(2)+2)) dx`
`=int (1)/((t+1) (t+2)) dt `
`"Let" x^(2) =t`
`rArr 2x dx =dt`
`"Now Let " (1)/((t+1)(t+2)) =(A)/(t+1) +(B)/(t+2)`
`=(A(t+2)+B(t+1))/((t+1)(t+2))`
`rArr A(t+2) +B(t+1)=1`
`"Put " t=-1`
`A(-1+2)+0=1 rArr A=1`
`"Put " t=-2`
`0+ B(-2+1) rArr B=-1`
`:. I= int (1)/(t+1) dt -int (1)/(t+2)dt`
`=log |t+1|-log |t+2|+c`
`=log |(x^(2)+1)/(t+2)| +c`
`=log |(x^(2)+1)/(x^(2)+2)| +c`
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