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Integrate the rational functions(3x-1)/...

Integrate the rational functions`(3x-1)/((x+2)^2)`

Text Solution

Verified by Experts

Let` (3x-1)/(x+2)^2`
​=`A/(x+2)+B/(x+2)^2`
⇒`3x−1=A(x+2)+B`
Equating the coefficient of x and constant term, we obtain
`A=3,2A+B=−1⇒B=−7`
So equating we get `(3x-1)/(x+2)^2=3/(x+2)−7/(x+2)^2`
⇒`∫(3x-1)/(x+2)^2=3∫1/(x+2)dx−7∫x/(x+2)^2dx`
=`3log∣x+2∣−7(-1/(x+2))+C`
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