How do you use partial fraction decomposition to decompose the fraction to integrate 4x−23(x−1)2?

1 Answer
Jim H
Jun 15, 2015

4x−23(x−1)2=13[4x−1+2(x−1)2]

Explanation:

4x−23(x−1)2=13⋅4x−2(x−1)2

So we really only need to decompose the second factor:

4x−2(x−1)2=Ax−1+B(x−1)2

=(Ax−A)+B(x−1)2

=Ax−A+B(x−1)2

So we need:

Ax−A+B=4x−2.

So A=4 and, since −A+B=−2, we get B=2

4x−23(x−1)2=13[4x−1+2(x−1)2]

∫4x−23(x−1)2dx=13[∫4x−1dx+∫2(x−1)2dx]

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