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Question

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

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Solution

Ondivinding(x2+1)by(x2+2x+1),weget(x2+1)(x+1)2={12x(x+1)2}Let2x(x+1)2=A(x+1)+B(x+1)22x=A(x+1)+B.(1)Onequatingthecoefficientsofx,wegetA=2Onequatingconstantterm,wegetA+B=0B=A=22x(x+1)2=2(x+1)2(x+1)2I={12x(x+1)2}={12(x+1)+2(x+1)2}dxx2log|x+1|2(x+1)+C.

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