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Evaluate: int(2x-3)/(x^2+6x+13)\ dx...

Evaluate: `int(2x-3)/(x^2+6x+13)\ dx`

Text Solution

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I=`int(2x-3)/(x^2+6x+13)\ dx`
`d/dx(x^2+6x+13)=2x+6`
Let `2x-3=A(2x+6)+B`
Thus,A=1,b=-9
I=`int(2x+6-9)/(x^2+6x+13)\ dx`
I=`int(2x+6)/(x^2+6x+13)\ dx-int(9)/(x^2+6x+13)\ dx`
=`int(2x+6)/(x^2+6x+13)\ dx-9int(1)/(x^2+6x+13)\ dx`
=`log(x^2+6x+13)-9int(1)/((x+3)^2+(2)^2)`
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