I know how to use this algorithm when I am integrating rational functions, but my textbook has omitt

Semaj Christian

Semaj Christian

Answered question

2022-06-21

I know how to use this algorithm when I am integrating rational functions, but my textbook has omitted the actual proof for why it works. If someone could please help me with this question:
Prove that given a and b, there are constants c 1 and c 2 so that
a x + b ( x 1 ) 2 = c 1 x 1 + c 2 ( x 1 ) 2

Answer & Explanation

Aaron Everett

Aaron Everett

Beginner2022-06-22Added 18 answers

c 1 x 1 + c 2 ( x 1 ) 2 = c 1 ( x 1 ) + c 2 ( x 1 ) 2 . Equating coefficients in c 1 x + ( c 2 c 1 ) = c 1 ( x 1 ) + c 2 = a x + b gives c 1 = a and c 2 c 1 = b so that c 2 = a + b.

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