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Evaluate: int(2x+3)/(x^2+3x+2)...

Evaluate: `int(2x+3)/(x^2+3x+2)`

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` (2x)/(x^(2)+3x+2)=(2x)/(x^(2)+2x+x+2)`
` =(2x)/(x(x+2)+1(x+2))`
`=(2x)/((x+2)(x+1))`
`" Let " (2x)/((x+2)(x+1)) =(A)/((x+2)) +(B)/((x+1))`
` rArr (2x)/((x+2)(x+1))=(A(x+1)+B(x+2))/((x+2)(x+1))`
`rArr 2x=A (x+1)+B(x+2)`
` x=-1 " then " -2 =0 +B (1) rArr B=-2`
`x=-2 " then " -4 =A(-1)+0 rArr A=4`
`:. int(2x)/((x+2)(x+1))dx`
` = int(A)/((x+2))dx +int(B)/((x+1))dx`
`=int(4)/((x+2))dx + int ((-2))/((x+1))dx`
`=4 log |x+2|-2log |x+1|+c`
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