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Integrate the rational functions1/(x^2-...

Integrate the rational functions`1/(x^2-9)`

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Let `1/((x+3)(x−3))​=A(x+3)​+B(x−3)`​
`⇒1=A(x−3)+B(x+3)`
Equating the coefficients of x and constant term, we obtain
`A+B=0,3A+3B=1`
On solving,
`A=(−1)/6​ and B=1/6​`
`∴1/((x+3)(x−3))​=(−1)/(6(x+3))​+1/(6(x−3))​`
`⇒∫(1​dx)/(x^2−9)=∫((−1)/(6(x+3))​+1/(6(x−3))​)dx`
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