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Evaluate: int(4x+1)/(x^2+3x+2)...

Evaluate: `int(4x+1)/(x^2+3x+2)`

Text Solution

Verified by Experts

I=`int(4x+1)/(x^2+3x+2)`
I=2`int(2x+3)/(x^2+3x+2)`-5`int(1)/(x^2+3x+2)`
let,
`x^2+3x+2=t`
`(2x+3)dx=dt`
So,
`I=2int (dt)/t-5 int(dx)/((x+3/2)^2-(1/2)^2)`
`I=2log(x^2+3x+2)-5 int(dx)/((x+3/2)^2-(1/2)^2)`
...
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