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Question

Integrate the following functions w.r.t. x.
x28x+4x34xdx

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Solution

x28x+4x34xdxLet x28x+4x34x=x28x+4x(x24)
=x28x+4x(x2)(x+2)
Let x28x+4x(x2)(x+2)=Ax+Bx2+Cx+2
x28x+4=A(x24)+B(x2+2x)+C(x22x)x28x+4=(A+B+C)x2+(2B2c)x4A
On comparing,
A+B+C=1,2B2C=8,4A=4
On solving, A=1,B=1,C=3
x2+8x+4x34xdx=11xdx1(x2)dx
=log|x|log|x2|+3log|x+2|+K

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