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

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

Text Solution

Verified by Experts

Let `I=int (2x)/((x^(2)+1)(x^(2)+2))dx`
Putting `x^(2)=t` and `2x dx=dt`, we get
`I=int (dt)/((t+1)(t+2))`
`=int((1)/(t+1)-(1)/(t+2))dt`
`=log|t+1|-log|t+2|+C`
`=log|x^(2)+1|-log|x^(2)+2|+C`
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