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Question

Integrate the rational function 3x1(x+2)2

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Solution

Let 3x1(x+2)2=A(x+2)+B(x+2)2
3x1=A(x+2)+B
Equating the coefficient of x and constant term, we obtain
A=3,2A+B=1B=7
3x1(x+2)2=3(x+2)7(x+2)2
3x1(x+2)2dx=31(x+2)dx7x(x+2)2dx
=3log|x+2|7(1(x+2))+C
=3log|x+2|+7(x+2)+C

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