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Evaluate int (3x-1)/((x-2)^(2))dx...

Evaluate `int (3x-1)/((x-2)^(2))dx`

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Verified by Experts

`" Let " (3x-1)/((x+2)^(2))=(A)/((x+2))+(B)/((x+2)^(2))`
`rArr (3x-1)/((x+2)^(2))=(A(x+2)+B)/((x+2)^(2))`
`rArr 3x-1 =A(x+2) +B`
`x=-2 " then " -6 -1 =0 +B rArr B=-7`
Equating the coefficients of x,
`3=A`
`:. (3x-1)/((x+2)^(2)) =(3)/((x+2)) -(7)/((x+2)^(2))`
`rArr int (3x-1)/((x+2)^(2))dx`
`= 3 int (1)/((x+2))dx-7 int(1)/((x+2)^(2))dx`
`=3 log |x+2|-7 ((-7)/(x+2))+c`
`=3 log |x+2| +(7)/(x+2)+c`
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