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Question

Evaluate
3x+1(x2)2(x+2)dx

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Solution

Let 3x+1(x2)2(x+2)=Ax2+B(x2)2+Cx+2
3x+1=A(x2)(x+2)+B(x+2)+C(x2)2
3x+1=A(x24)+B(x+2)+C(x24x+4)
A+C=0A=C
B4C=3,4A+2B+4C=12B+8C=1
Solving these we get B=74,C=516,A=516
3x+1(x2)2(x+2)dx=516dxx2+74dx(x2)2516dxx+2=516ln|x2|74(x2)516ln|x+2|

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