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Evaluate: intx/(x^2+3x+2)\ dx...

Evaluate: `intx/(x^2+3x+2)\ dx`

Text Solution

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`I=``intx/(x^2+3x+2)\ dx`
`I=1/2``int(2x+3-3)/(x^2+3x+2)\ dx`
`I=1/2``int(2x+3)/(x^2+3x+2)\ dx`-`3``int3/(x^2+3x+2)\ dx`
let `x^2+3x+2=t`
`(2x+3)dx=dt`
so,
`I=1/2int(dt)/t-3/1 int(dx)/((x+2)(x+1))`
`I=1/2log(t)-3/2 int((x+2-x-1)/((x+2)(x+1)))`
...
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