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Integrate the rational functionsx/((x+1...

Integrate the rational functions`x/((x+1)(x+2)`

Text Solution

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Let `x/((x+1)(x+2))​=A(x+1)​+B(x+2)`​
`⇒x=A(x+2)+B(x+1)`
Equating the coefficients of x and constant term, we obtain
`A+B=1,2A+B=0`
On solving, we obtain
`A=−1 and B=2`
`∴x/((x+1)(x+2))​​dx=(−1)/(x+1)​+2/(x+2)​`
`⇒∫x/((x+1)(x+2))​dx=∫(-1)(x+1)​+2/(x+2)​dx`
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